https://mw.lojban.org/api.php?action=feedcontributions&user=Krtisfranks&feedformat=atomLojban - User contributions [en]2019-11-14T18:30:39ZUser contributionsMediaWiki 1.30.0https://mw.lojban.org/index.php?title=Talk:experimental_rafsi&diff=123409Talk:experimental rafsi2019-08-19T21:08:58Z<p>Krtisfranks: Preliminary version of table</p>
<hr />
<div>{| class="wikitable sortable"<br />
! Serial Number !! Proposed rafsi !! Proposed assigned selrafsi !! Experimental rafsi class !! Selrafsi category !! Conflicts !! Proposed by !! Other notes !! See also<br />
|-<br />
| 1 || zil || zi'o || 0: Mostly-Official: in gismu list, not in rafsi list || official cmavo || || || Missing from rafsi list, but is explicitly mentioned and assigned in official publications. || <br />
|-<br />
| 2 || jax || jai || 1: Proposed and Unofficial || official cmavo || || || || <br />
|-<br />
| 3 || jaz || jai || 1: Proposed and Unofficial || official cmavo || || || || <br />
|-<br />
| 4 || nej || nei || 1: Proposed and Unofficial || official cmavo || || || || <br />
|-<br />
| 5 || kib || kibro || 1: Proposed and Unofficial || experimental gismu - popular || || || || <br />
|-<br />
| 6 || niz || nai || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Choose no more than three rafsi for "nai" at any given time. || <br />
|-<br />
| 7 || nij || nai || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Choose no more than three rafsi for "nai" at any given time. || <br />
|-<br />
| 8 || nai || nai || 1: Proposed and Unofficial || official cmavo || Y || Krtisfranks || Reassignment would be required; choose no more than three rafsi for "nai" at any given time. || <br />
|-<br />
| 9 || nax || nai || 1: Proposed and Unofficial || official cmavo || Y || Krtisfranks || Reassignment would be required; choose no more than three rafsi for "nai" at any given time. || <br />
|-<br />
| 10 || jix || ji || 1: Proposed and Unofficial || official cmavo || || || || <br />
|-<br />
| 11 || jiv || ji || 1: Proposed and Unofficial || official cmavo || jinvi || Krtisfranks || Reassignment would be required. Follows pattern for JA. See "jinvi" entry. Would have preference over, but would not necessarily preclude, "-jix-" for "ji". || <br />
|-<br />
| 12 || jni || jinvi || 2: Proposed and Unofficial; phonotactics changes required. || official gismu || || Krtisfranks || "jn" is currently not a permitted initial consonant cluster. Preferably, unassign "-jiv-" from "jinvi" if "-jni-" is adopted for the same. || <br />
|-<br />
| 13 || faf || fa || 1: Proposed and Unofficial || official cmavo || || Selpahi/Tsani || Proposed by Selpahi/Tsani ( http://selpahi.weebly.com/archive/a-list-of-new-rafsi ); endorsed by Krtisfranks. In a series. || <br />
|-<br />
| 14 || fef || fe || 1: Proposed and Unofficial || official cmavo || || Selpahi/Tsani || Proposed by Selpahi/Tsani ( http://selpahi.weebly.com/archive/a-list-of-new-rafsi ); endorsed by Krtisfranks. In a series. || <br />
|-<br />
| 15 || fif || fi || 1: Proposed and Unofficial || official cmavo || || Selpahi/Tsani || Proposed by Selpahi/Tsani ( http://selpahi.weebly.com/archive/a-list-of-new-rafsi ); endorsed by Krtisfranks. In a series. || <br />
|-<br />
| 16 || fof || fo || 1: Proposed and Unofficial || official cmavo || || Selpahi/Tsani || Proposed by Selpahi/Tsani ( http://selpahi.weebly.com/archive/a-list-of-new-rafsi ); endorsed by Krtisfranks. In a series. || <br />
|-<br />
| 17 || fuf || fu || 1: Proposed and Unofficial || official cmavo || || Krtisfranks/Selpahi/Tsani || "Implied to be (but not explicitly) proposed by Selpahi/Tsani<br />
|-<br />
| ( http://selpahi.weebly.com/archive/a-list-of-new-rafsi ); explicitly proposed by endorsed by Krtisfranks. In a series." || <br />
|-<br />
| 18 || fox || fai || 1: Proposed and Unofficial || official cmavo || || Selpahi/Tsani || Proposed by Selpahi/Tsani ( http://selpahi.weebly.com/archive/a-list-of-new-rafsi ); endorsed by Krtisfranks. In a series. || <br />
|-<br />
| 19 || duv || dau || 1: Proposed and Unofficial || official cmavo || || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). || <br />
|-<br />
| 20 || fel || fei || 1: Proposed and Unofficial || official cmavo || || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). || <br />
|-<br />
| 21 || gam || gai || 1: Proposed and Unofficial || official cmavo || || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). || <br />
|-<br />
| 22 || juz || jau || 1: Proposed and Unofficial || official cmavo || || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). || <br />
|-<br />
| 23 || xem || xei || 1: Proposed and Unofficial || experimental cmavo - popular || || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). See "xei". || <br />
|-<br />
| 24 || xem || rei || 1: Proposed and Unofficial || official cmavo || || ? || Proposed by .rab.spir. In a sorta-series (hex digits). Does not share consonant with selrafsi, but allows for flexibility in 'dialect' (assuming that 'xei' = 'rei'). || <br />
|-<br />
| 25 || rex || rei || 1: Proposed and Unofficial || official cmavo || rexsa || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). "rexsa" as selrafsi potentially proposed first. || <br />
|-<br />
| 26 || vav || vai || 1: Proposed and Unofficial || official cmavo || || .rab.spir. || Proposed by .rab.spir. In a sorta-series (hex digits). || <br />
|-<br />
| 27 || tex || te'o || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Proposed by Krtisfranks. Preferably, both "-tex-" and "-tez-" would be adopted. || <br />
|-<br />
| 28 || tez || te'o || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Proposed by Krtisfranks. See "tezda"; preferably, both "-tex-" and "-tez-" would be adopted. || <br />
|-<br />
| 29 || cix || ci'i || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 30 || xix || xi || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 31 || xon || xo'ei || 1: Proposed and Unofficial || experimental cmavo || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 32 || xox || xo || 1: Proposed and Unofficial || experimental cmavo - popular || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 33 || || || || || || || || <br />
|-<br />
| 34 || **** DID NOT DO ANYTHING BETWEEN "coi doi ro do mi'e .telsekik." and ".i .a'o ro do plitce" (as of 19 Aug 2019 at 8:00 a.m. ET)!!!!!!!!!!!!!!!!!! || || || || || || || <br />
|-<br />
| 35 || || || || || || || || <br />
|-<br />
| 36 || || || || || || || || <br />
|-<br />
| 37 || || || || || || || || <br />
|-<br />
| 38 || xro || xrotu || 1: Proposed and Unofficial || experimental gismu || || Selckiku(?) || Proposed by Selckiku(?). The selrafsi (which is itself experimental) is in conflict with experimental gismu "xlotu". || <br />
|-<br />
| 39 || glo || glotu || 1: Proposed and Unofficial || experimental gismu || || Selckiku(?) || Proposed by Selckiku(?). Jbovlaste does not have record of the selrafsi. || <br />
|-<br />
| 40 || xlo || xlotu || 1: Proposed and Unofficial || experimental gismu || || Selckiku(?) || Proposed by Selckiku(?). The selrafsi (which is itself experimental) is in conflict with experimental gismu "xrotu". Jbovlaste does not have record of the selrafsi. || <br />
|-<br />
| 41 || va'a || va'arga || 1: Proposed and Unofficial || zevla || || || zevla rafsi || <br />
|-<br />
| 42 || .i ra'oi -zvi- rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack)) || || || || || || || <br />
|-<br />
| 43 || (Others in this region of the page; see next tab in this workbook) || || || || || || || <br />
|-<br />
| 44 || jos || jonse || 1: Proposed and Unofficial || experimental gismu || || Sphenicine || Proposed by Sphenicine || <br />
|-<br />
| 45 || dit || ditcu || 3: Proposed and Unofficial - has history/notable usage || experimental gismu - removed prior to baselining || || Xorxe/Selpahi/others || gismu was removed prior to gismu list baselining; re-proposed by Xorxes; Selpahi proposed the rafsi, but it was already in some use - further history of the rafsi is unknown to Krtisfranks. || <br />
|-<br />
| 46 || sus || smusu || 1: Proposed and Unofficial || experimental gismu || || Sphenicine || Proposed by Sphenicine || <br />
|-<br />
| 47 || sem || su'ei || 1: Proposed and Unofficial || experimental cmavo || || Gleki || Proposed by Gleki || <br />
|-<br />
| 48 || zve || zevla || 1: Proposed and Unofficial || experimental gismu - popular || || || || <br />
|-<br />
| 49 || toz || to'ai || 1: Proposed and Unofficial || experimental cmavo || || Selpahi || Proposed by Selpahi. In a series. || <br />
|-<br />
| 50 || voz || vo'ai || 1: Proposed and Unofficial || experimental cmavo || || Selpahi || Proposed by Selpahi. In a series. || <br />
|-<br />
| 51 || xoz || xo'ai || 1: Proposed and Unofficial || experimental cmavo || || Selpahi || Proposed by Selpahi. In a series. || <br />
|-<br />
| 52 || pom || po'o || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Proposed by Krtisfranks. Has better combinatory power than "-pov-". || <br />
|-<br />
| 53 || pov || po'o || 1: Proposed and Unofficial || official cmavo || || Selpahi/Tsani || Proposed by Selpahi/Tsani. Has worse combinatory power than "-pom-". || <br />
|-<br />
| 54 || rex || rexsa || 1: Proposed and Unofficial || experimental gismu || rei || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 55 || coc || corci || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 56 || nif || nicfa || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 57 || gav || grava || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 58 || vul || vubla || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 59 || xig || xigzo || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 60 || mug || mugle || 1: Proposed and Unofficial || experimental gismu || Y || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 61 || xob || xonba || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 62 || gul || gugle || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 63 || vaf || valfa || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 64 || zic || zmico || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 65 || zu'a || zucna || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 66 || zna || zucna || 2: Proposed and Unofficial; phonotactics changes required. || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. "zn" is not a permitted initial consonant cluster; if it becomes so, then this proposal is made (and, possible, "zu'a" should be unassigned). || <br />
|-<br />
| 67 || tso || dutso || 1: Proposed and Unofficial || experimental gismu || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 68 || ___ || kamre || (N/A) || experimental gismu || (N/A) || (N/A) || (N/A) || <br />
|-<br />
| 69 || pef || pe'a || 1: Proposed and Unofficial || official cmavo || || Krtisfranks || Proposed by Krtisfranks. || <br />
|-<br />
| 70 || cox || co'ai || 1: Proposed and Unofficial || experimental cmavo || || Misotanis || Proposed by Misotanis. || <br />
|-<br />
| || || || || || || || || <br />
|-<br />
| || || || || || || || || <br />
|-<br />
| || || || || || || || || <br />
|-<br />
| || || kanpe || || || || || || <br />
|-<br />
| || || kosmu || || || || || || <br />
|-<br />
| || || krali || || || || || || <br />
|-<br />
| || || kinfi || || || || || || <br />
|-<br />
| || || kinra || || || || || || <br />
|-<br />
| || || takni || || || || || || <br />
|-<br />
| || || kloje || || || || || || <br />
|-<br />
| || || grafu || || || || || || <br />
|-<br />
| || || kipsi || || || || || || <br />
|-<br />
| || peg || pegva || || || || || || <br />
|-<br />
| || || paxra || || || || || || <br />
|-<br />
| || || jviso || || || || || || <br />
|-<br />
| || || pevna || || || || || From "pe'a"? || <br />
|-<br />
| || dit || dinti || || || || || || <br />
|-<br />
| || || katci || || || || || || <br />
|-<br />
| || || jmice || || || || || || <br />
|-<br />
| || || karpa || || || || || || <br />
|-<br />
| || || tutle || || || || || || <br />
|-<br />
| || || kapli || || || || || || <br />
|-<br />
| || || maska || || || || || || <br />
|-<br />
| || || || || || || || see "kesfi"; also develop word for "flipper, wing, paddle, oar, turbine blade". || <br />
|-<br />
| || || kesri || || || || || || <br />
|-<br />
| || || pilda || || || || || || <br />
|-<br />
| || || grava || || || || || || <br />
|-<br />
| || || dicma || || || || || || <br />
|-<br />
| || || vubla || || || || || || <br />
|-<br />
| || || tsaba || || || || || || <br />
|-<br />
| || || xigzo || || || || || || <br />
|-<br />
| || || jikfi || || || || || || <br />
|-<br />
| || || junta || || || || || || <br />
|-<br />
| || || tolfa || || || || || || <br />
|-<br />
| || || fizbu || || || || || || <br />
|-<br />
| || || fisli || || || || || || <br />
|-<br />
| || || jikfi || || || || || || <br />
|-<br />
| || || flese || || || || || || <br />
|-<br />
| || || mapra || || || || || || <br />
|}</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123407experimental rafsi2019-08-19T13:24:51Z<p>Krtisfranks: /* Proposed and Unofficial */ -- added "-cox-"</p>
<hr />
<div>== Introduction and Classification ==<br />
<br />
Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
Additionally, this page tends to focus on individual, atomic, and self-contained proposals which do not have larger effects, proposals, projects, or ideas behind them - with notable exceptions for series (such as for hexadecimal digits, drag-and-drop selbri-conversion, FA, etc.); in time, hopefully, additional discussions which touch on or which would be strongly affected by experimental rafsi can be added or linked to (such as in a "See Also" section).<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
**: Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
***: No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
***: ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-tez-'''" for "{{jvs|te'o}}" also. See: "{{jvs|tezda}}".<br />
** "'''-cix-'''" for "{{jvs|ci'i}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
** "'''-xox-'''" for "{{jvs|xo}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gav-'''" for "{{jvs|grava}}".<br />
* "'''-vul-'''" for "{{jvs|vubla}}".<br />
* "'''-xig-'''" for "{{jvs|xigzo}}".<br />
* "'''-mug-'''" for "{{jvs|mugle}}".<br />
* "'''-xob-'''" for "{{jvs|xonba}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
* "{{jvs|kamre}}" probably could use a cmarafsi too, but I ([[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]])) am not sure what to do for it at present (20:18, 9 September 2018 (UTC)).<br />
<br />
* "'''-pef-'''" for "{{jvs|pe'a}}". -- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 18:44, 10 January 2019 (UTC)<br />
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* "'''-cox-'''" for "{{jvs|co'ai}}" per la .misotanis. .<br />
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=== Experimental "-goi-" and "-zoi-" usages ===<br />
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* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
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This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.<br />
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== See Also ==<br />
<br />
* [[Proposal: "no"-"nu" Transposition]]. The cmavo "no" and "nu" would have their definitions mutually exchanged. The meanings of the rafsi would, therefore, be mutually exchanged as well. However, the forms of the rafsi are not altered.<br />
* [[Proposal: Drag-and-Drop Conversion Becomes Default]]. The meanings of "te" and "to'ai", of "ve" and "vo'ai", and of "xe" and "xo'ai" would each - respectively - be transposed; as such, the proposal also would redefine (but not reassign) the rafsi of each of these words so as to match their new meanings; "se" / "-sel-" would not be affected.<br />
* [[ce ki tau jau]]. Has numerous implications for rafsi, depending on which changes are implemented.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Extended_Dimensionality_of_Interval_cmavo&diff=123222Extended Dimensionality of Interval cmavo2019-05-23T17:21:13Z<p>Krtisfranks: /* Proposed Extension A: "mi'i" */ -- typos</p>
<hr />
<div>{{jbocre/en}}<br />
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Presently, the cmavo "mi'i", "bi'i", "bi'o" (which currently constitute all elements of selma'o BIhI) all represent/create one-dimensional intervals. However, in mathematics and even in daily life, there are many instances when higher-dimensional intervals are desired. This functionality should be supported.<br />
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Rather than creating new cmavo for this task, the current cmavo (aforementioned) can simply be extended. The proposal described here will have the objective of supporting functionality for description of higher-dimensional intervals via extension only; only mathematical points are being discussed. The result should be back-compatible.<br />
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== Contributors ==<br />
<br />
The following people have contributed to the writing of this article (or have provided ideas for it):<br />
*lai .krtisfranks.<br />
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Where first-person personal pronouns are used, they refer to at least one of these individuals. However, they will be avoided whensoever possible (with explicit mention of the author's name when a personal opinion or insight is conveyed).<br />
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== Current Functionality ==<br />
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The cmavo of BIhI are nonlogical interval connectives. In mathematics (other options are available), one inputs a real number or possibly a generic endpoint, follows it by a cmavo of BIhI, and then mentions another real number or endpoint. The result is a description of a set of all points belonging to an interval. More explicitly:<br />
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Let x and y be real numbers or points in geometric space, let r be a nonnegative real number. Let the space to which x and y belong be X. Further suppose that X does not "loop around" in any sense. Then:<br />
*x mi'i r: generates the interval centered on x which has range r on either side of x; in other words, this is the set of all points that have a distance to x that is less than (or possibly equal to) r. x is the midpoint of the interval, which has length 2r. Such a thing is sometimes denoted in a fashion similar to <math> \operatorname{B}_1 (x, r) </math>, where "B" is for "ball" and the subscript "1" tells the dimensionality of the space; this is also called an r neighborhood of x (sometimes denoted <math> \operatorname{nbhd} (x, r) </math>), where the space is inferred from context.<br />
*x bi'i y: generates the interval or unordered line segment with endpoints x and y; in other words, this is the set of all points between x and y (possibly including either, both, or neither of the endpoints). "y bi'i x" is completely equivalent to "x bi'i y"; there is no inherent order to the inputs nor direction to the line segment. This is the generic meaning for "between" when referring to an interval, in normal life or in mathematics; there is no notation for this notion which is both commonly understood and known to lai .krtisfranks. ; supposing an ordering on X, the closest thing would be an interval of form: <math>(\operatorname{min}(\{x,y\}), \operatorname{max}(\{x,y\})) \cup A</math>, where <math>A \subseteq \{x,y\}</math>. However, if X is a partially ordered space with order relation '<', then we may describe it thusly: let 'R' denote either '<' or its complement/negative '>'; then, if the endpoints are excluded, "x bi'i y" generates the set <math> \{ \alpha \in X: x </math> R <math> \alpha </math> R <math> y \} </math>. (Notice here that x and y may be presented in either order but for any given selection of presentation order, 'R' is fixed in meaning and present in both relations; if one order of presentation is true, then if the order is switched, then the resulting statement will mean the same thing but the meaning of 'R' will be changed to the other inequality relation. If an endpoint is to be included, this set will just be united with the singleton set of that endpoint. If X cannot be or is not partially ordered, then this present discussion about mathematical representation may be ignored; in such cases, this BIhI construction may still make sense, however - just revert to a more intuitive understanding based on the English description).<br />
*x bi'o y: generates the interval or 'directed' line segment with endpoints x and y in that order (starting from x and going to y); otherwise, it is equivalent to "bi'i". This is the typical meaning of intervals of form [x, y) and the like. Thus "y bi'o x" is backward relative to "x bi'o y". Continuing the discussion in the immediately previous point about "bi'i" which was concerned with nathematical representation of the construct formed, and supposing the same conditions and notation, then "x bi'o y" is exactly the same (and the same commentary applies) except that it demands that 'R' represents '<'. (Notice additionally that, in this case, x < y must be true. However be careful to avoid reading "<" as the symbol representing "less than" in the intuitive sense for real numbers; it could just as easily be any other partial order, including the "greater than" relation).<br />
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When X does not "loop around" through the initially-potential intervals in question (it may do so through others): "bi'i" has a symmetry between its two arguments. Thus, it would be weird for conditions to be placed on exactly one of its arguments. "bi'o" is a restriction of "bi'i" which forces a directionality or order upon the line segment produced; thus "bi'o" inherits properties from "bi'i" but the broken symmetry allows conditions to be placed on any combination of its arguments in a natural context.<br />
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If X does "loop around" through at least one initially-potential interval at hand, then: "bi'i" forces the 'most natural' or 'minimal' interval to be the one which is being referenced under either ordering of the inputes, and "bi'o" results in the 'most natural' or 'minimal' interval which extends '''from''' the first argument '''to''' the second argument. For example, on a circle, where angles are measured counterclockwise (from the positive x-axis, toward the positive y-axis; an angle of measure <math>0</math> has its rays both being equivalent to the positive x-axis) and where the arguments refer to points on the circle by the angles so measured from the positive x-axis (in radians) at which they are located (modulo <math>\tau = C/r</math> for circle of circumference <math>C</math> and radius <math>r>0</math>): "<math>0</math> bi'o <math>\tau/4</math>" is equivalent to "<math>0</math> bi'i <math>\tau/4</math>" (and, therefore, "<math>\tau/4</math> bi'i <math>0</math>", which is the single arc segment which forms one quarter of the entire circle and which is between the positive x-axis and the positive y-axis; but "<math>\tau/4</math> bi'o <math>0</math>" is entirely different, being the other three quarters of the circle (and, if it matters, this is traced out via having the angle run counterclockwise from positive y-axis (at <math>\tau/4</math>) until it attains the value <math>\tau \equiv 0</math> at the positive x-axis (from 'the other side', so to speak). Throughout this article, X will typically be assumed to not 'loop around' through any initially-potential interval at hand, but the considerations made in this paragraph should apply without too much difficulty in making the analogy.<br />
* (Note that "initially-potential interval" is interpreted broadly, accounting for all conceivable references intended for the interval at hand, which means that X 'loop around' through at least one of the results of "bi'o" and of "se bi'o" for the given arguments (in fixed order); the set of such potential intervals are those which could be meant prior to the audience actually thinking too deeply about the meaning/structure (it is the set of all initial interpretations which are conceivable, regardless of whether they are possible). In this sense, an interval is a path from one of the arguments to the other. Consider a graph/network G of points with some edges. It might be the case that G is a tree (lacks any loops) except for, say, exactly one loop (a sequence of edge-connected nodes such that there is at least one path from at least one node to itself via the edges) which includes a proper subset of its nodes, numbering at least two (for simplicity). As long as both "bi'o" and "se bi'o" do not intersect nonemptily with any of the nodes/edges in this loop, then the loop can be 'excised' from consideration and we can take X to not loop around through any of the initially-potential intervals; in other words X would be the result of 'subtracting' the loop from G; such a subtraction would have no impact on the interval actually meant. On the other hand, if at least one of those intervals does indeed intersect nonemptily with the loop, then X must be taken to 'loop around' through at least one initially-potential interval at hand, and this potential 'looping' must be taken into account when interpreting/evaluating the meaning of the interval being specified).<br />
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Suppose that X does not loop through any initially-potential interval at hand.<br />
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It should be noted that, unless <math>x = \pm \infty</math> is defined and true in a given case, <math>\forall r \in [0, + \infty]</math>, "x mi'i r" refers to/forms a bounded interval or the whole space; no semi-infinite (that is: bounded from above/the positive side xor from below/the negative side) interval/line segment (ray) can be produced. The same is true for "bi'i" and "bi'o" if, additionally, r is finite; recall the previous commentary about symmetry of arguments and inheritance concerning these words. These proposals - where '<math>\infty</math>' now refers to any point which has a distance of <math>+ \infty</math> from the origin - will (or, at least, thus far have) not change(d) this fact. In both the current (non-proposed) functionality and the herein proposed functionality, the intervals which are produced by "bi'i" and "bi'o" can be bounded, semi-infinite (in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)), or infinite in both positive and negative directions (doubly-infinite/infinite; in any number of directions (so long as that number is a nonnegative integer less than or equal to twice the dimensionality of the space)); in the herein proposed functionality, these states can be simultaneously true, with the interval being semi-infinite in some dimensions, infinite in others, and bounded/finite in yet others (the total count of such dimensions being equal to the dimensionality of the space).<br />
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If we accept partial orders, the space X can be all sorts of creatures, including - for example - sets under the strict-containment/proper-subset relation (so that BIhI forms an interval of sets). However, more exotic meanings can be used/intended (although any partial order endowing the space would have to be ignored in context with respect to the meaning of BIhI, which is okay and implicitly possible within the description heretofore provided by the CLL). For example, intervals may just trace out (a possibly ordered/'directed') path between points in X, which may be - for example - the geography of locations on Earth, a network, or a set of sets (which may otherwise but inconsequentially for our purposes be endowed with the proper-subset order). In order to be clear: X need not have an order of any kind endowing it overall; however, if "bi'o" is used, the interval generated does have an ordered endowed on it (alone) which may or may not match the order endowing X, should such an order exist.<br />
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A final note for the sake of carefulness: "bi'o" establishes an order on a line segment such that its first argument is somehow 'less' than its second one. However, it does not necessarily/really establish a direction on the line segment in a graph theoretic sense. So, throughout this page, take mentions of directionality with a grain of salt - they may be the result of momentary carelessness.<br />
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=== SE BIhI ===<br />
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Although independent of this whole proposal, SE (specifically "se" and "re'au'e") should be able to precede BIhI. For "bi'i" itself, there would be no effect. For "se bi'o", the order of the arguments is switched so that the first argument of "se bi'o" is the greater/destination endpoint and the second argument thereof is the lesser/origin endpoint. Thus, "bi'i" is equivalent to "bi'o ja se bi'o". For "se mi'i", the order of the arguments is switched so that the first represents the radius length (in one-dimension: half of the length of the linear interval) and the second represents the center of the interval.<br />
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== Proposed Functionality ==<br />
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Any commentary in this article (excluding the 'Authors' and 'Current Functionality' sections) is meant to be taken as part of the "whole proposal". What follows are specific details which are broken into labelled sections for the sake of reference and hierarchy of application.<br />
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=== Main Proposal #1 ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; fix a basis B thereof. Let r be a nonnegative real number. Let x and y live in the same space X. Define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity. Define B = {<math>e_1, e_2, ..., e_n</math>}. Then there exists <math> x_1, x_2, ..., x_n, y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n), y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let "''R''" denote an 'ordering' relation on F or the ordered field of real numbers (as appropriate) which may be either the "less than" relation (denoted "<") or, as appropriate (determined by GAhO; generically, elliptical), the "less than or equal to" relation (denoted "<math>\leq</math>").<br />
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We let the dimensionality of our space (which is and can be inferred from the dimensionality of x and/or y, which should match) determine the nature of our intervals.<br />
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* "mi'i" is the easiest to redefine. In fact, the previous description needs no reworking, so long as we understand the space to be potentially larger than a line and loosen our notion of "interval". I propose that "x mi'i r" is defined to be/describe the n-dimensional hyperball (or, possibly, the closure thereof) which is centered on/at x and which has radius r. Notationally, it is <math>\{ z \in X: d(x,z)</math> ''R'' <math>r \}</math>.<br />
** In order to be clear: this interval is a neighborhood in the space; that is to say, it is a region of the space which is bounded by and internal to a sphere (but which may possibly include the boundary and/or exclude the center). This region is called a "ball".<br />
** I propose that we adopt additional keywords/glosses/terminology for "mi'i". "mi'i" should be given the keyword/gloss "centered interval"; it might also deserve the keyword/gloss "n-ball". The second argument (here denoted by "r") should be called the "radius" (in addition to "range"). The first argument (here denoted by "x") can remain with the sole label of "center".<br />
* "bi'i" requires a little more work. I propose that "x bi'i y" generates/describes the n-cell/n-orthotope which has opposite vertices at points x and y. This is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (x_i</math> ''R'' <math> \alpha_i </math> ''R'' <math> y_i)) \}</math>.<br />
** This is similar to the rectangle made on a computer by clicking the mouse at one endpoint and holding-with-dragging the cursor to the other endpoint. Note that there are as many ways to generate the same 'rectangle' as there are vertices on/of the 'rectangle' (where this jumber scales with dimensionality of the 'recrangle'). It need not be two-dimensional, though.<br />
** Terminology can again be updated (id est: added to). The interval should be additionally described as a "n-cell" and "n-orthotope interval"; "rectilinear interval" may additionally be considered. Both arguments (here denoted by "x" and "y" respectively) should be labelled as "endpoints". Symmetry between them should be noted in dictionary definitions.<br />
** This extended form of "bi'i" can be obtained via Cartesian products of linear intervals aligned with/generated by the basis elements. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
* "bi'o" has, to me (lai krtisfranks), no obvious extension since (for example) <math>\mathbb{R}^2</math> cannot be ordered.<br />
<br />
_<br />
<br />
When <math>F = \mathbb{R}</math>, 1-tuples/1-dimensional endpoints will be isomorphically mapped automatically to the corresponding real numbers. This allows for ease of use and back-compatibility.<br />
* This is done by establishing the identity/correspondence that <math>\forall (\xi) \in F, (\xi) \leftrightarrow \xi </math>. In other words, the functionality of intervals as defined outside of this whole proposal (which is for the 1-dimensional case) is extended so that endpoints "x" and "y" which are scalars are automatically mapped to (x) and (y) respectively, where the latter are now handled via the extended functionality herein proposed (as a point in (albeit one-dimensional) space and which has coordinates (well, exactly 1 coördinate)).<br />
<br />
Notice that, now, "mi'i" and "bi'i" do not have the same "shape" except when the dimensionality involved is 0 or 1. The former is round whereas the latter is rectilinear. This is assuming Euclidean geometry. If other netrics are involved, they may appear to be the same or may actually be the same. For example, in taxicab geometry, a sphere <i>appears</i> to be a cross-polytope of the appropriate dimensionality, yet it is still a sphere (which bounds "mi'i"-intervals). In Chebyshev geometry, a sphere appears as an orthotope of the appropriate dimensionality, yet it is still a spehere (and the boundary of a "mi'i"-interval); in this case, though, it very well may be congruent to the n-cell (orthotope) that "bi'i" produces (under the proper conditions).<br />
* These distinct definitions are good (utile) and natural in theoretical mathematics.<br />
<br />
=== Alternative #1: Line Segments Unless Specified Otherwise ===<br />
<br />
An alternative (which lai .krtisfranks. finds perhaps even better than the previous proposal (Main Proposal #1)) is to have "bi'i" and "bi'o" always default to referencing line segments (generally: geodesics) in any space. That is, regardless of the space, these two cmavo (but not "mi'i") would 'draw' a line from their first argument to their second one.<br />
<br />
Note: The endpoints (first and second arguments) of "bi'i" and "bi'o" will be points that are specified via multiple coördinates with respect to a basis. They are not merely scalars. They still must live in the same space (X) and thus must have the same number of coördinates. In this situation, the one-dimensional usage which is defined already outside of this whole proposal merely isomorphically maps scalars which are denoted by "x" and "y" to the their corresponding 1-dimensional point specifications "(x)" and "(y)" respectively. (Notice that, without an additional convention, these will never map to "(x,0,0,...)" and "(y,0,0,...)" respectively, despite the isomorphism that may be established. This is meant to avoid the abusive mixing of notation/spaces: there is no interval from (1,2) to 1, for example. We should always specify that the endpoints are higher-dimensional. This note about mapping 1 to (1) is meant solely for the purpose of making this extension back-compatible and natural.)<br />
<br />
This would make the default usage automatically compatible with generalized points (see below). Additionally, line segments are generally useful in geometry of any (nontrivial) dimension, so this functionality would be utile.<br />
<br />
This also would allow both "bi'i" and "bi'o" to be defined in any decent space (as opposed to only have "bi'i" be defined, which is the case in the aforementioned subproposal).<br />
<br />
In this formulation, "x bi'o y" implies that x is in some sense a starting point of reference/of an imaginary journey and y is the corresponding termination point; both are 'endpoints'/terminals, so to speak. If the space does not 'loop around', then the set produced, however, is still exactly equivalent to that produced by "x bi'i y" and any coloring of the connotations is unmathematical (and, thus, should be avoided in the opinion of lai .krtisfranks.),; the latter is generally preferred.<br />
<br />
Note: There is still no established directionality on the linear interval that is produced by "bi'o". However, as long as it does not conflict with any others, we might be able to assume an established order thereupon. "x bi'o y" does mean that "x < y" (along that line).<br />
<br />
In this case, we use "ce'ei'oi" (followed by a number larger than 1 if we are being explicit) on either or both points x, y in the constructs "x bi'i y" and "x bi'o y" in order to produce the swept-out higher-dimensional-orthotopal "interval" that was proposed originally. See the 'Handling Generalized Points' section, following, for more details.<br />
<br />
"mi'i" will still generalize to a higher-dimensional-ball in the space. (Its functionality, as described previously, and as extended immediately after this section, is unchanged.)<br />
<br />
=== Proposed Extension A: "mi'i" ===<br />
<br />
"mi'i" can be extended further. Keep the previous definitions and conditions. Now, undefine r. Let <math>r_1, r_2, ..., r_n \geq 0</math>.<br />
<br />
Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coördinates of points in X with respect to the basis established. Note that r does not live in X; it is just a formal n-tuple which has entries ordered in a corresponding manner - in other words, it is just a list of numbers (scalars in the underlying field, more specifically) with the order of presentation fixed by the basis of X and according to the utterer's intention. Notice that r does not technically change if the basis is changed; in such a situation, it may not be possible to describe the n-dimensional interval in simple terms (using only linear combinations of the entries of the new basis) at all and, in any case, the utterer would generally need to supply an entirely different list <math> r\prime </math> in order to convey the same thought.<br />
<br />
* Then we can define "x mi'i r" as <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (d_F (x_i, \alpha_i)</math> ''R'' <math>r_i)) \}</math>. Notice that 'd' is now actually '<math>d_F</math>', id est: the metric on the field F. Here, each coordinate of a point <math>\alpha</math> is being compared to the corresponding coordinate of point x; if they are within the specified distance of one another (given by the corresponding entry in the list r), then that coordinate works out; iff all of the coordinates of the point work out, then the point belongs to the interval so described.<br />
** This extended form of "mi'i" can be obtained via Cartesian products of linear intervals. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
<br />
This essentially returns us to the old situation wherein the interval is no longer an n-ball but an n-cell (matching "bi'i"). The side lengths vary (being <math>2 r_i</math> in length, for each side i). The lines which pass through their corresponding/respective midpoints and which are perpendicular to the corresponding hyperfaces will intersect at a single point, videlicet the first argument of "mi'i" constructs (the 'center'; more appropriately: circumcenter), which is the point from which the various perpendicular distances to the boundaries are each measured (being <math> r_i </math>, for the appropriate/corresponding i).<br />
<br />
This definition is good for computer science, graphing, and experimental science. It is almost never used in theoretical mathematics. (Literally never in the experience of lai .krtisfranks., at any rate.)<br />
<br />
This additional proposal requires no major update, change, or addition to the glossing/keywords associated with "mi'i" in dictionary definitions, although there would be an implicit understanding of increased generality. If desired, however, "orthotopic interval with given circumcenter" or similar would do nicely.<br />
<br />
* Additionally, we could establish the convention-by-definition that: <math>((\exists \rho \geq 0: ((\forall i \in \mathbb{N} \cap [1, n]), (r_i = \rho))) \implies </math> "x mi'i r" = "x mi'i <math>\rho</math>" <math>)</math>; but we would need a way to ensure that the audience recognizes <math>\rho</math> as an n-tuple and not just a scalar. Otherwise, utilization of this convention would be indistinguishable from the previously-mentioned case/proposal wherein the second argument as a single number constitutes the radius of an n-ball.<br />
** This complication can be overcome by mentioning "ce'ei'oi" immediately after "<math>\rho</math>" (list sense) in the "mi'i" construct; if this is done, then we are to understand that "<math>\rho</math>" represents - in short-hand form - a formal tuple of identical entries (each being <math>\rho</math> (in the scalar sense)). The elements of this tuple must never be negative.<br />
*** If the utterer explicitly defines/declares <math>\rho</math> to be such a formal tuple, then "ce'ei'oi" is not necessary, although it is also not wrong (and may in fact be helpful and encouraged).<br />
<br />
== Handling Generalized Points ==<br />
<br />
If the input (x and y; the type of one determines the type of the other by forcing it to be the same) are generalized points (such as towns/geographic points), then they likely live in at-least-two-dimensional space, as is the case on Earth. However, with or without Alternative #1, they are being treated as distinct points (assigned real numbers isomorphically if Alternative #1 is not adopted; otherwise, they are free to be points in space). According to this proposal, it is not possible for the interpretation of an interval with these arguments to be anything except one-dimensional. But, for example, maybe we want to discuss the 'rectangular' (more on this immediately later/below) area of the globe between Olympia, Washington, U.S.A. (defined as x) and Tallahassee, Florida, U.S.A. (defined as y). (This rectangle covers much of the continental/contiguous U.S.) "x bi'i y" would, presumably, give the quickest route for a roadtrip or flight from Olympia to Tallahassee (the geodesic line segment (more on this immediately later/below)) or the reverse thereof (from the other to the one); it would not yield the 'rectangle' that we want. The word "ce'ei'oi" fixes this issue. If it is used on a generalized point (rather than a formal tuple - see immediately previous/above ("mi'i" discussion)), then it indicates that that endpoint (and, consequently, all others) is to be treated multi-dimensionally (unless the argument of "ce'ei'oi" is identically and exactly equal to 1). (In order to be clear: in "mi'i", the second argument (the tuple of "radius length(s)") is not considered to be an endpoint for this purpose - or, truly, anywhere within this proposal; it has a distinct nature and possibly typing separate from that of the first argument of "mi'i".) It is not necessary if Alternative #1 is not adopted and if the points are already defined to belong to a well-described space (of known dimensionality) or are decomposed in terms of their basis/represented as a tuple. If we do this, with the former definitions, then "x ce'ei'oi bi'i y" will suddenly indicate not the line(ar interval) between x and y, but instead the 'area between them'. (This area may be visualized thusly: Imagine a map with x and y on it, on a computer. Click on one of these points, drag the cursor to the other. In many programs, a (possibly degenerate) rectangle is swept out, usually with a dashed or dotted outline. The opposite corners of this rectangle are x and y; the remaining corners are given by one coordinate of x and the other coordinate of y, as appropriate. The space highlighted (within this rectangle) is the interval formed.)<br />
<br />
Note that "x ce'ei'oi bi'i y" is equivalent to "x ce'ei'oi bi'i y ce'ei'oi" and to "x bi'i y ce'ei'oi". Likewise if we replace "bi'i" with "bi'o".<br />
<br />
Note that "ce'ei'oi" has to follow the last argument of "bi'i" and "bi'o" when it is used therein and on the right/later side of BIhI and if the right/later BIhI argument is a scalar of nonnegative integer value; else, it will adopt the BIhI argument as its own (instead), unless its own argument is immediately followed by "boi".<br />
<br />
The space in which this interval exists is determined by context. This is a problem even in the unextended (one-dimensional) version of these words in this usage: Is the unordered interval from Paris to London along the Earth's surface (geodesic) or is it a straight line through space (intersecting the Earth's surface at some points as well as the interior)? Is the (un)ordered interval, if geodesic, following the shorter segment of the great-circle connecting the two cities, or the longer one? (The same is true in and with Alternative #1 each.)<br />
<br />
Note that in any case x and y need to live in the same space. So, if one is a generalized point, then the other must be. It makes no sense to discuss the interval from 1 to you or from Olympia to my imaginary friend. Moreover, they must have the same dimensionality; placing "ce'ei'oi" on one of them determines the nature of the other (and so is unnecessary); however, the argument of "ce'ei'oi" does need to be compatible with both x and y if present (for "bi'i" and "bi'o"; this is not the case for its being used upon the first argument of "mi'i", but is indeed the case in its being used on the second argument of "mi'i").<br />
<br />
== Endpoint Clusivity Stati (Inclusion/Exclusion) ==<br />
<br />
=== Notation, Background, Set-Up ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity; fix a basis B = {<math>e_1, e_2, ..., e_n</math>} thereof. Let x and y live in the same space X. Then there exists <math> x_1, x_2, ..., x_n,\; y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n),\; y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let <math>\rho,\; r_1, r_2, ..., r_n \geq 0</math>. Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just an n-tuple which has entries ordered in a corresponding manner. If n = 1, then we denote: x = (x) = (<math>x_1</math>), y = (y) = (<math>y_1</math>), r = (r) = (<math>r_1</math>).<br />
<br />
Assume at least some of the previous proposals.<br />
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In this section, "endpoint status" (plural: "endpoint stati") and "clusivity" will refer to the options that an utterer has in specifying whether or not the boundary of the (multidimensional) interval is included xor excluded (along certain hyperplanes/manifolds). If such a boundary is included, then we call it "inclusive", "open", "soft", and "rounded" (due to the notation of using rounded brackets ("(" and ")") or an open circle ("○") in graphical/visual depictions). If such a boundary is excluded, then we call it "exclusive", "closed", "hard", and "square"/"sharp" (due to the notation of using square brackets ("[" and "]") or a closed circle ("●") in graphical/visual depictions). Fix an order '<' on the one-dimensional space(s) to at least one of which every linear interval is taken to belong; in each case of occurrence, appropriately redefine "''R''" <math>\in \{ ``<", ``\leq" \}</math> as determined by intent and context.<br />
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A bracket is a symbol which is used in order to denote a piece of the boundary of an interval. It also encodes endpoint status (id est: the clusivity of that part of the boundary). We use rightward-opening brackets for those which, in 1 dimension, bound the space from below/the negative side; these are "(", "[", and "【". "(" denotes such a boundary which is open; "[" denotes such a boundary which is closed; "【" will be used herein as a short-hand way of denoting the general such boundary which may, depending on context, be replaced with "(" and/or "["; this last is called a(n) (opening/rightward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. We use leftward-opening brackets for those which, in 1 dimension, bound the space from above/the positive side; these are ")", "]", and "】". ")" denotes such a boundary which is open; "]" denotes such a boundary which is closed; "】" will be used herein as a short-hand way of denoting the general such boundary which may be, depending on context, be replaced with ")" and/or "]"; this last is called a(n) (closing/leftward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. If it is not clear (especially with the usage of the lenticular brackets, which can assume various values depending on context and which may or may not be interdependent), brackets which pair or depend upon one another will be subscripted with the same label/index as appropriate.<br />
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The status of "【" or of "】" is which of the two options (inclusive or exclusive) it represents in a given instant/context. The status of ''R'' is which of "<" or "<math>\leq</math>" it represents in a given instant/context.<br />
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"<math>\times</math>" denotes the Cartesian product of sets. For sets A and B, <math> A \times B = \{ (a, b):\; a \in A \;\&\; b \in B \}</math>, where (a,b) is a tuple/point with coordinates (namely, in order: a, b) rather than, as the unfortunate notation may suggest, a linear interval from a to b. Note that it is ordered and not commutative. It can be made into a big/serial/iterating operator, denoted: "<math> \times_{i \in C} </math>", where i is an index and it takes every value in a set C subject to the order on C (if there is any).<br />
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Denote: <math>\mathbb{N} \cap [1, n] = \boxdot (n)</math>.<br />
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This section will use "ce'ei'oi" throughout its body. This is done for the sake of eliminating ambiguity and compatibility with all proposals (and alternatives) herein presented.<br />
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Terminology: In "x mi'i r" (for any dimension for x regardless of r) we call x the "center" and r the "radius (length)". Note that, even though it may be called "radius", r really refers to the length in a given dimension. (Radii are really line segments, not the lengths which are associated with them; we abuse terminology here for simplicity.) Any point which has distance from the center (according to the appropriate metric) in a given direction which is exactly equal to the appropriate radius length in the same direction is called an "on-sphere point", "outermost points", or "distant point" of the interval in question. The set of all on-sphere points of an interval is its "outer boundary" or "(outer/minimal enclosing) sphere". Note that "mi'i" may actually generate an n-orthotope (per Proposed Extension A) and thus may not seem or be spherical; the terminology does not vary in order to explicitly and individually account for such cases. The center of a "mi'i" interval is an element of the boundary (which is, generally, partitioned into outer and inner parts; the center is the sole element of the inner part thereof); thus, the center is an endpoint with a clusivity status.<br />
<br />
Terminology: Each (n-1)-side of the n-orthotope produced via interval constructs will be called a "boundary-part" (these are the aforementioned hyperplanes segments); these generalize the notion of "endpoints" (in a slightly different way from how the arguments of BIhI do so) from the one-dimensional case. They may still be called "endpoints" in this article, even though they are not actually points. For a given interval, the set of all such boundary-parts thereof is the boundary of the interval. "mi'i" is taken to have a whole and indivisible outer boundary (without individual boundary-parts) when its dimensionality is greater than 1; when its dimensionality is equal to 1, the two outermost (end)points may be taken to each constitute a boundary-part of the outer boundary; there is an additional (inner) boundary-part, which is exactly the singleton set of the center point.<br />
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''''!'''' '''Important Result''': The n-orthotope formed by "x ce'ei'oi bi'i y (ce'ei'oi)" is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (x_i</math> ''R'' <math>_{-1,i} \alpha_i </math> ''R'' <math>_{1,i} y_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>, where: <math>\forall i \in \boxdot (n)</math>, the status of '【<math>_{i}</math>' is determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{-1,i}</math>' and likewise the status of '】<math>_{i}</math>' is analogously determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{1,i}</math>'.<br />
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=== Current Situation: the One-Dimensional Case ===<br />
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This section is according to (an interpretation of) the CLL.<br />
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In one dimension, we can specify the status of either endpoint of the (linear) interval via use of members of GAhO immediately next to the member of BIhI being used, on the appropriate side. For example, "li no ga'o bi'o ke'i li pa" represents the interval [0, 1). Notice that "ga'o" (which specifies an inclusive endpoint/boundary-part on the negative side) is on the leftern/first-uttered side of "bi'o" (id est: immediately preceding it) and follows "li no"; this means that the lesser endpoint (in this case, the point 0) is to be included. Likewise, "ke'i" (which specifies an exclusive endpoint/boundary-part) is on the rightern/last-uttered side of "bi'o" (id est: immediately following it) and precedes "li pa"; this means that the greater endpoint (in this case, the point 1) is to be excluded.<br />
<br />
The exact same is true if we replace "bi'o" with "bi'i", although we will lose the implication that <math>0 \leq 1</math>.<br />
<br />
Members of GAhO, at least in BIhI constructs, seem to be used - if at all - only adjacent to the member of BIhI itself. lai .krtisfranks. does not know if they are used in any other context or in any other way. There seems, to lai .krtisfranks, to be no recognition nor convention concerning how to interpret the absence of any explicit members of GAhO on one or both sides of BIhI. It does not seem possible, to lai .krtisfranks., for multiple members of GAhO or of BIhI to consecutively succeed one another (of the same selma'o) whilst being 'naked' (id est: with their dictionary meaning, without being quoted or deleted, without being JE- or JOI-connected, etc).<br />
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The structure of a BIhI construct is: [endpoint<sub>1</sub>] (GAhO*) BIhI* (GAhO*) [endpoint<sub>2</sub>].<br />
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=== Assumption/Proposal anent Unmentioned GAhO ===<br />
<br />
The content of this section may count as an additional proposal. In any case, it is assumed throughout the rest of the article.<br />
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If, between an argument of BIhI and the BIhI cmavo itself, there is no explicitly mentioned member of GAhO, then one is still assumed to be present and to apply to and only to the appropriate boundary-part; the clusivity content of an implicit GAhO cmavo, such as in this case, is elliptical/unspecified/vague - it may or may not be determined by context, practicality, or intent, or it may be unimportant (thus, possibly, representative of either possibility).<br />
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For your information: "xau'u'oi" is a member of GAhO which is elliptical with respect to clusivity (status), as described immediately previously. It is proposed separate from and independent of/to this whole proposal or any of its parts. However, the two complement eachother well.<br />
<br />
Whether implicit (as described herein) or explicitly elliptical, such an elliptical clusivity status will be denoted by lenticular brackets in linear intervals.<br />
<br />
It does not make sense for a nontrivial interval of dimensionality at least 1 to neither include nor exclude any given boundary-part in the current framework of what is easily supported and expressible by Lojban; even mathematically and independent of the language, such a statement is true if it is restricted to the one-dimensional case (with end-'''points'''). Therefore, we must assume that one xor the other case applies. Thus, it should not be contentious that this assumption is made.<br />
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=== Proposed Extension B: GAhO with "mi'i", a simple case ===<br />
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There appears to be no prior usage of GAhO with "mi'i" except as proposed [[BPFK Section: Intervals|here]], a notion which lai .krtisfranks. separately formulated in his considerations for this article. The suggestion there is as follows:<br />
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GAhO before "mi'i" indicates the "endpoint status" of the center of the interval. "ga'o" there indicates that the center (the entire internal boundary-part) is definitely included (thereby forming a continuous/contiguous linear interval); the radius-distanced endpoints may or may not be included. "ke'i" there indicates that the center is definitely excluded (thereby forming a broken/punctured linear interval which misses only its center and possibly the radius-distanced endpoints). This usage in nondegenerate cases has no bearing on the clusivity of the radius-distanced endpoints (unless one specifies explicitly that these stati are mutually determinable).<br />
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GAhO after "mi'i" indicates the endpoint status of any point which has distance from the center exactly equal to the radius length specified. "ga'o" here indicates that all of the on-sphere points of the interval are definitely included (causing the outer boundary of the interval to be included; this is pictorially represented by a solid boundary curve). "ke'i" here indicates that all of the on-sphere points of the interval are definitely excluded (causing the outer boundary of the interval to be excluded; this is pictorially represented a dashed/dotted/broken boundary curve). Notice that every on-sphere point shares the same status as every other on-sphere point of a given interval. In nondegenerate cases, this usage has no bearing on the clusivity status of the center of the specified interval (unless one specifies explicitly that these stati are mutually determinable).<br />
<br />
These descriptions apply for the one-dimensional case, but generalize - with little change - to arbritrary dimensionality. The only difference is that the interval generated will be a possibly-punctured line (segment), disc, ball, glome interior, or - generally - n-ball, depending on the dimensionality.<br />
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<br />
Let <math> x \in \mathbb{R}</math>. So, <math> x \leftrightarrow (x)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. These are all one-dimensional:<br />
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* "x mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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<br />
* "x ga'o mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ke'i mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
<br />
<br />
* "x mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
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* "x mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
<br />
<br />
* "x ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
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* "x ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) < \rho \}</math>.<br />
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* "x ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) \leq \rho \}</math>.<br />
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* "x ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) < \rho \}</math>.<br />
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<br />
_<br />
<br />
For emphasis: Even though the forms of the mathematical expressions are approximately the same (similar on first glance) to the analogous expressions for "bi'o", and despite the formal similarities in the Lojban utterances, it is important to realize that <math>\rho</math> here is '''not''' an endpoint of the linear interval. The presence of 'd' in the definition makes a world of difference.<br />
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=== Main Proposal #2 ===<br />
<br />
Recall: dim(X) = n.<br />
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Note: In this section, it is taken to be the case that two mutually adjacent members of GAhO do not compound to form a member of GAhO* (in/as which they cannot be separated).<br />
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<br />
<br />
<br />
It would be nice to be able to specify the status of boundary-parts of higher-dimensional intervals. But there is a great deal of customizability that is available. The pair "vau'e'oi" and (its elidable terminator) "vau'o'oi" handle this.<br />
<br />
The way that they work is as follows:<br />
# "vau'e'oi" opens a scope; this is called the "interval brackets scope" (hereby named "(the) IBS"). The IBS is closed via explicit use of "vau'o'oi", or immediately upon the utterance of any word which is not a member of selma'o GAhO*, or immediately upon the event of the number of explicitly utterred GAhO* members exceeding n. Thus, the only words which may belong within the IBS are members of GAhO* and they number at most n. Any GAhO cmavo explicitly used immediately after the nth explicitly used one in an IBS is ignored.<br />
# The IBS has n ordered slots; these are called "IBS slots" (or, here, just "slots"). Initially, no slots are filled. For each IBS slot, a single explicitly utterred member of GAhO* can fill it. Once one slot is filled, the next explicitly utterred GAhO* member fills the next available slot if possible/it is available. The first explicitly utterred GAhO* member fills the first IBS slot. Members of GAhO* do not need to be separated nor connected from one another in any way. They are Quine-quoted and treated as separate entities '''automatically'''. Thus, no explicit quotes are necessary.<br />
# If the IBS is closed 'prematurely' (id est: before n GAhO* members are explicitly utterred), then any IBS slot which is not explicitly filled at this point is taken to be filled by a vague/elliptical value.<br />
# Syntactically, the IBS result is treated as a single occurrence of GAhO*. Thus the IBS construct must be adjacent to an explicit member of BIhI.<br />
# Semantically/practically, the result is a formal and ordered tuple of interval brackets, the elements of which are the brackets supplied to the IBS in order such that the <math>i</math>th element of the formal tuple produced being the bracket supplied to the <math>i</math>th IBS slot. The location of this result relative to the adjacent BIhI member forces the nature of these brackets (to be rightward-opening iff the result is utterred before/is to the left of the adjacent BIhI member; to be leftward-opening iff the result is utterred after/is to the right of the adjacent BIhI member). Denote this result to be <math>(</math>''B''<math>_1, ...,</math>''B''<math>_n)</math>. Notice that this usage of the character "B" is not the same as elsewhere in this article (where it, for example, may have meant a particar basis); here, it is an individual bracket with a defined clusivity status. The role of this bracket is determined by the location of its IBS with respect to the relevant BIhI; its particular realization with respect to that boundary - that is, its applicability to one or more boundary-parts in that boundary - is determined by the slot which it fills and the basis determined by context.<br />
# The <math>i</math>th member of this tuple (namely, ''B''<math>_i</math>) acts as the corresponding bracket (opening or closing, open or closed) for the <math>i</math>th (component-)interval (parallel to the <math>i</math>th basis element) in the Cartesian product reëxpression/decomposition of the overall interval if such is possible. In other words, the clusivity of the ith hyperplane is that of the bracket B<sub>i</sub>. The order is important and corresponds via index.<br />
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Reiterating: An IBS of n > 0 slots that is closed while having only m slots explicitly filled by GAhO*, where 0 < m < n and m is an integer, has the last n-m slots filled implicitly by an elliptical GAhO* element (with restrictions intuitively/implicitly placed upon it due to context). Notice that GAhO cmavo connected by JE or JOI, for example, form a single element of GAhO* for the purpose of filling slots. There is no separator between filled slots; the GAhO* elements may just be rattled off, separated automatically and filling the slots successively.<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> ce'ei'oi (<math>n</math>) vau'e'oi 【<math>_{1}</math> 【<math>_{2}</math> ... 【<math>_{n}</math> (vau'o'oi) bi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(y_1, y_2, ..., y_n)</math> (ce'ei'oi (<math>n</math>))", where <math>(x_1, x_2, ..., x_n)</math> and <math>(y_1, y_2, ..., y_n)</math> are expressed with respect to the basis of the space.<br />
**Notice the lack of commas/separators between brackets. Also note that only one occurrence of "ce'ei'oi" is necessary in this case (since we are working with "bi'i"). The usage of "vau'o'oi" here (in both cases) is optional.<br />
** Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (\alpha_i \in </math>【<math>_i\; x_i,\; y_i </math>】<math>_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>.<br />
*** Thus, we see that the <math>i</math>th opening bracket goes with <math>x_i</math> and the <math>i</math>th closing bracket goes with <math>y_i</math>.<br />
*** Even though it has the same generic form as was expressed in the final part of the previous "Current Functionality" subsection, the meaning is rather different. There, the brackets were elliptical/vague/generic/general. Here, they are specified by the utterrer to be whatsoever was said in the IBS.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> ce'ei'oi (ci) vau'e'oi ga'o ke'i ga'o (vau'o'oi) bi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(y_1, y_2, y_3)</math> (ce'ei'oi (ci)).<br />
** Then <math>I = [x_1 ,\; y_1) \times (x_2 ,\; y_2) \times [x_3 ,\; y_3]</math>. This is the basically the referent of "vei <math>x_1</math> ga'o bi'i ke'i <math>y_1</math> ve'o pi'u vei <math>x_2</math> ke'i bi'i ke'i <math>y_2</math> ve'o pi'u vei <math>x_3</math> ga'o bi'i ga'o <math>y_3</math> ve'o".<br />
<br />
Note that in the precious two examples, so order was imposed on each linear subspace of X. This can be done, mathematically. But it was done here for convenience/for the sake of having established notation in order to make sense of the meaning in a rigorous way. If such order exists on a given linear subspace of X, then all is well for that particular instance of its imposition. However, when interpreting, one must remember to "unimpose"/"unassume" such an ordering. The linear intervals are just specified by two endpoints; the endpoints themselves can be switched (especially systematically). This, however, is a reasonable and semi-canonical way to represent the linear intervals (as long as one remembers that the endpoints need no be in the specified order); it would be confusing to switch only some of them.<br />
<br />
Moral of the story: The IBS causes the brackets that it is given to be sent off to couple with the coordinate to which they belong, in order.<br />
<br />
Postliminarily: It is not grammatical to have naked members of GAhO uttered consecutively in a BIhI construct except when they all are in an IBS (as enclosed by "vau'e'oi" and (possibly elided) "vau'o'oi").<br />
<br />
=== Further Proposal: a Nice and Simple Case for Brackets ===<br />
<br />
The content of this section supposes Main Proposal #2 as being accepted and applicable.<br />
<br />
In this section, back-compatibility, utility/ease, and a simple and nice case are handled.<br />
<br />
What if we do not want to say all of that? How do we support back-compatibility this way? What if all of the brackets submitted is a certain IBS are the same? Well, here is some more functionality: If the last case holds and if "ce'ei'oi" is mentioned so as to apply to an endpoint (rather than a radius length(s) entry), then we can dispense with the IBS altogether. In the multidimensional case, a single bracket ''B'' on a given side of "bi'i" is taken to be isomorphic with the formal ordered interval-bracket tuple (''B'', ..., ''B''), where the number of entries therein is the dimensionality of the space n. Id est: each GAhO cmavo actually constitutes an n-slot IBS such that every entry in it is, explicitly, that very same cmavo. Therefore, "vau'e'oi vau'o'oi" is equivalent to a single instance of "xau'u'oi" alone, allowing for n-dimensionality; this in particular is back-compatible with earlier claims/assumptions/proposals.<br />
<br />
In the case of all the brackets on one side being (of) the same (status), we can just call the tuple by the name of the shared bracket (status). If we are working in an n-dimensional space and we are given only one bracket B outside of an IBS on a given side of "bi'i" explicitly, then we know that the IBS actually should should actually contain n brackets of form B (of the same status). This can work simultaneously on both sides of BIhI.<br />
<br />
In short: "ce'ei'oi n ga'o bi'i" is equivalent to "ce'ei'oi n vau'e'oi ga'o ga'o [...] ga'o vau'o'oi bi'i", where "ga'o" is explicitly mentioned n times in the latter sentence. Analogy/substitution for other cases (such as: using "ke'i", having the brackets on the other side of the BIhI cmavo, or using another cmavo in BIhI) follows by the syntactic uniformity within selma'o.<br />
<br />
Thus, <math>\forall x, y \in \mathbb{R}</math>, "x ga'o bi'i y" is mapped isomorphically to "x (ce'ei'oi pa) vau'e'oi ga'o (vau'o'oi) bi'i (vau'e'oi (vau'o'oi)) y". Recall, of course, that "x" here actually maps to "(x)" isomorphically too, and likewise for "y"; this detail was not shown for clarity, since parentheticals were employed in that example/string in order to represent optional utterrances, and the endpoints are definitely not optional in general.<br />
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Further: At most one naked member of GAhO which is not enclosed by an IBS xor at most one IBS may be explicitly used on a given side of BIhI; any more of either and/or the use of both together is ungrammatical.<br />
<br />
=== Proposed Extension B' ===<br />
<br />
This section assumes adoption of Proposed Extension B. If anything is to be done with "mi'i" (even in the 1-dimensional case) this subproposal (respectively Proposed Extension B) needs to be accepted.<br />
<br />
In "mi'i", the first bracket never needs to be processed through an IBS. Either the center point is included or excluded, and this can be handled one-dimensionally (id est: by just using a member of GAhO on its own). Only one first bracket can be used/appear.<br />
<br />
If "mi'i" is being used in order to produce/describe an n-ball (rather than an n-orthotope, per Proposed Extension A), then only one second (formally "closing") bracket can be used/appear, and- thus- it need not be processed through an IBS. In this case, every on-sphere point is either included xor they are all excluded; specification of this status can be handled one-dimensionally (id est: by just using a member of GAhO on its own).<br />
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<br />
<br />
Let <math> x \in X</math>. So, <math> x = (x_1, ..., x_n)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. "R" is used, as before, for an inequality relation that may be either strict or loose (the latter admits the possibility for equality). These are all n-dimensional:<br />
<br />
* "x (ce'ei'oi (n)) mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball which may or may not include its external boundary (but whatsoever it does there, it does so to the totality thereof).<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is an unpunctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ke'i mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a punctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
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<br />
* "x (ce'ei'oi (n)) mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely united with its sphere (boundary); it would be drawn with a solid surface on the outside.<br />
* "x (ce'ei'oi (n)) mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely not united with its sphere (boundary); it would be drawn with a broken/dashed/dotted surface on the outside.<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
** This is a closed (solid) unpunctured disc/ball; it definitely includes both its center and its external boundary; it would be drawn with a solid surface on the outside and shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) < \rho \}</math>.<br />
** This is an open unpunctured disc/ball; it definitely includes its center but definitely excludes it external boundary; it would be drawn with a broken/dashed/dotted surface but with shading throughout the interior.<br />
** This is the typical definition of "ball" (or "disc" in two dimensions). It has only interior points, but it has all of them.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) \leq \rho \}</math>.<br />
** This is a punctured disc/ball which is united with its external sphere (external boundary); it definitely includes its external boundary but definitely excludes its center; it would be drawn with a solid surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) < \rho \}</math>.<br />
** This is a punctured disc/ball which excludes its external sphere (external boundary); it definitely excludes both its external boundary and its center; it would be drawn with a broken/dashed/dotted surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
** This is the typical definition of a punctured ball (disc in two dimensions). It is useful for the definition of limit points in topology.<br />
<br />
<br />
Clearly, as before, the definitions extend exceptionally easily for this interpretation of "mi'i". In the mathematics, the only formal change in the condition was replacing each "<math>\mathbb{R}</math>" with <math>X</math>. Of course, the points themselves have multiple coordinates and thus the meaning of 'd' gets slightly more complicated, but that is all under the hood (determined by the definition of 'd' and/or intuition about what would be appropriate for the space, given X itself).<br />
<br />
=== Proposed Extension C ===<br />
<br />
This section assumes adoption of Proposed Extension A and Proposed Extension B' (and thus Proposed Extension B).<br />
<br />
If working with "mi'i" where the first argument <math>x = (x_1, ..., x_n)</math> lives in n-dimensional space and if the second argument <math>r = (r_1, ..., r_n)</math> is a formal ordered tuple of n nonnegative extended-real numbers, then an n-cell is produced, in which case "vau'e'oi" and "vau'o'oi" work exactly as before (with "bi'i"). But it is important to note that the IBS can be nontrivial only on the second-argument side of "mi'i".<br />
<br />
Throughout this section, "d" still denotes a distance function on the space X.<br />
<br />
<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 mi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>(x_1, x_2, ..., x_n)</math> is expressed with respect to the basis of the space (and represents a point therein) and <math>r</math> formally corresponds via indices coordinatewise.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.<br />
** If, here, '【' = '(' here, let <math>C = \{ (x_1 , x_2 , x_3) \} </math>, id est the singleton of the central point; if, here, '【' = '[', then let <math> C = \{ \} </math>. Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in [0,\; r_i </math>】<math>_i)) \} \setminus C</math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ga'o (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3]</math>.<br />
*** Notice that, despite the inclusion status of the first argument, the leftern brackets in the Cartesian expression of this orthotope have varied clusivity status. The important thing is that the intervals are continuous (not missing their central point x<sub>i</sub>) due to the explicit presence of "ga'o" immediately before "mi'i"; the clusivity stati of the leftern bracket and of the rightern bracket in each Cartesian-productand should mutually match - and they are determined determined by the member of GAhO in the corresponding ISB slot in the ISB immediately following "mi'i".<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ke'i (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = \big( (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3] \big) \setminus (x_1 , x_2 , x_3 ) </math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = ((x_1 - r_1 ,\; x_1) \cup (x_1 ,\;x_1 + r_1)) \times ((x_2 - r_2 ,\; x_2) \cup (x_2 ,\;x_2 + r_2)) \times ([x_3 - r_3 ,\; x_3) \cup (x_3 ,\;x_3 + r_3])</math>.<br />
<br />
== Vocabulary/Semantics that have been Introduced ==<br />
<br />
Mostly, old vocabulary has been expanded in functionality.<br />
<br />
'''Old/CLL vocabulary with expanded functionality''':<br />
*mi'i - Originally, this word denotes/construct a line or line segment which was (taken to be) centered on the point specified by the first argument and which had length specified by the second argument. Main Proposal #1 allows "mi'i" to denote/construct a volume in n dimensions which is bounded by a sphere which is centered at the point specified by the first argument and which is of the radius specified by the second argument. Proposed Extension A allows "mi'i" to denote/construct a volume enclosed by an n-orthotope with axes parallel to those of the space (the basis) such that each side has a distance from the point, specified by the first argument, which is equal to the corresponding entry in the list which is specified by the second argument; if all entries in the list which is the second argument are the same, then the second argument may be represented by just that number via the use of "ce'ei'oi" (see later).<br />
*bi'i - Originally, this word denotes/constructs a line, linear ray, or line segment in one-dimensional space between two specified points (rays have one such point being infinite; lines have both being infinite). Main Proposal #1 extends the functionality so that this word denotes/constructs a volume enclosed by an n-orthotope in n-dimensional space (which may have any, all, or none of its faces/sides at infinity), such that each axis thereof is parallel to one axis of the space (defined by a single element of the basis); the two arguments of "bi'i" specify some pair of mutually opposite vertices on the n-orthotope - there coordinates with respect to the relevant basis determine the corresponding sides and are the corresponding endpoints in an expression of the generated volume by Cartesian product of one-dimensional linear intervals (which may be given by CLL/old "bi'i" itself).<br />
*bi'o - Originally, this word acted as "bi'i" does with the further assumption that the first argument is lesser/the origin and the second argument is greater/the destination. Its functionality was not really generalized in this whole proposal.<br />
*ga'o/ke'i - If every bracket in an IBS (see "vau'e'oi", later) would be explicitly specified as a single particular member of GAhO, then the whole IBS may be abbreviated to/represented by a single instance of the same unenclosed in an IBS.<br />
<br />
For all of these, if the points specified are one-dimensional, generic/geographic, or cannot be specified in terms of a tuple of coordinates (as given by the basis of the space), then they may be represented by a simple point/name (not enclosed in a tuple), which is isomorphic to a one-tuple of only that entry.<br />
<br />
<br />
'''New vocabulary''':<br />
<br />
*ce'ei'oi<br />
*vau'e'oi<br />
*vau'o'oi<br />
*IBS<br />
<br />
'''Independent vocabulary''':<br />
<br />
*xau'u'oi<br />
<br />
== Miscellany ==<br />
<br />
"mi'i" is really good for error bars in the sciences. In English, scientists often say stuff like "g is 9.85 plus-or-minus .05 meters per second per second". This is abusive. The only options for the value of g in such a case would be 9.80 m/s<sup>2</sup> or 9.90 m/s<sup>2</sup>. What they mean is that the value of g is between these two values (possibly including either of them). Following the format of the example quote, we have "mi'i" being the intention, with 9.85 functioning as the center and .05 as the radius. In describing a data set, one should make sure to say that the variable (usually dependent) ''belongs'' to this set, rather than it ''being'' this set. This variable will be the one with error bars in the graph. If a single variable is described in such a manner, the error bars graphically are parallel to only one axis: the actual value (as measured, within standard deviation/error) can shift in this direction (so long as it remains within the bars) but cannot shift in any other. If the error bars are applied to the ''point'', rather than the ''variable'' (which acts as a coordinate of the former), though, then the error bar will (under this proposal) envelop the point in a ball of the given radius; the actual value (as measured, within standard deviation/error) could thus shift in any direction within n-space so long as it remains within the provided radius of the given (measured, central) value. Adopting Proposed Extension A, each coordinate can be individually and independently assigned/associated with an error; the error bars will graphically be parallel to each axis (or will be 0); the actual value (as measured, within standard deviation/error for each measurement/variable/coordinate) can shift relative to the data point along each axis so long as it stays within the axis-appropriate radius of the data point.<br />
<br />
=== Further Ideas ===<br />
<br />
* It may be beneficial to us to figure out a system by which to generate basic shapes such a convex hulls via specification of important points (or sets of points). The current framework does not support such generalization since only two arguments of BIhI are presently allowed.<br />
<br />
* We may want a separate word for or modifier of "mi'i", here denoted by "<u>'''NTRVL'''</u>", such that: for <math>I \prime</math> being the interval generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 <u>'''NTRVL'''</u> vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>x = (x_1, x_2, ..., x_n) \in X</math> is expressed with respect to the basis of the space <math>X</math> (and represents a point therein) and <math>r = (r_1, r_2, ..., r_n)</math> formally corresponds via indices coordinatewise, then <math>I \prime = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Extended_Dimensionality_of_Interval_cmavo&diff=123221Extended Dimensionality of Interval cmavo2019-05-23T15:57:22Z<p>Krtisfranks: /* Alternative #1: Line Segments Unless Specified Otherwise */ - minor corrections</p>
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<div>{{jbocre/en}}<br />
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Presently, the cmavo "mi'i", "bi'i", "bi'o" (which currently constitute all elements of selma'o BIhI) all represent/create one-dimensional intervals. However, in mathematics and even in daily life, there are many instances when higher-dimensional intervals are desired. This functionality should be supported.<br />
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Rather than creating new cmavo for this task, the current cmavo (aforementioned) can simply be extended. The proposal described here will have the objective of supporting functionality for description of higher-dimensional intervals via extension only; only mathematical points are being discussed. The result should be back-compatible.<br />
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== Contributors ==<br />
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The following people have contributed to the writing of this article (or have provided ideas for it):<br />
*lai .krtisfranks.<br />
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Where first-person personal pronouns are used, they refer to at least one of these individuals. However, they will be avoided whensoever possible (with explicit mention of the author's name when a personal opinion or insight is conveyed).<br />
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== Current Functionality ==<br />
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The cmavo of BIhI are nonlogical interval connectives. In mathematics (other options are available), one inputs a real number or possibly a generic endpoint, follows it by a cmavo of BIhI, and then mentions another real number or endpoint. The result is a description of a set of all points belonging to an interval. More explicitly:<br />
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Let x and y be real numbers or points in geometric space, let r be a nonnegative real number. Let the space to which x and y belong be X. Further suppose that X does not "loop around" in any sense. Then:<br />
*x mi'i r: generates the interval centered on x which has range r on either side of x; in other words, this is the set of all points that have a distance to x that is less than (or possibly equal to) r. x is the midpoint of the interval, which has length 2r. Such a thing is sometimes denoted in a fashion similar to <math> \operatorname{B}_1 (x, r) </math>, where "B" is for "ball" and the subscript "1" tells the dimensionality of the space; this is also called an r neighborhood of x (sometimes denoted <math> \operatorname{nbhd} (x, r) </math>), where the space is inferred from context.<br />
*x bi'i y: generates the interval or unordered line segment with endpoints x and y; in other words, this is the set of all points between x and y (possibly including either, both, or neither of the endpoints). "y bi'i x" is completely equivalent to "x bi'i y"; there is no inherent order to the inputs nor direction to the line segment. This is the generic meaning for "between" when referring to an interval, in normal life or in mathematics; there is no notation for this notion which is both commonly understood and known to lai .krtisfranks. ; supposing an ordering on X, the closest thing would be an interval of form: <math>(\operatorname{min}(\{x,y\}), \operatorname{max}(\{x,y\})) \cup A</math>, where <math>A \subseteq \{x,y\}</math>. However, if X is a partially ordered space with order relation '<', then we may describe it thusly: let 'R' denote either '<' or its complement/negative '>'; then, if the endpoints are excluded, "x bi'i y" generates the set <math> \{ \alpha \in X: x </math> R <math> \alpha </math> R <math> y \} </math>. (Notice here that x and y may be presented in either order but for any given selection of presentation order, 'R' is fixed in meaning and present in both relations; if one order of presentation is true, then if the order is switched, then the resulting statement will mean the same thing but the meaning of 'R' will be changed to the other inequality relation. If an endpoint is to be included, this set will just be united with the singleton set of that endpoint. If X cannot be or is not partially ordered, then this present discussion about mathematical representation may be ignored; in such cases, this BIhI construction may still make sense, however - just revert to a more intuitive understanding based on the English description).<br />
*x bi'o y: generates the interval or 'directed' line segment with endpoints x and y in that order (starting from x and going to y); otherwise, it is equivalent to "bi'i". This is the typical meaning of intervals of form [x, y) and the like. Thus "y bi'o x" is backward relative to "x bi'o y". Continuing the discussion in the immediately previous point about "bi'i" which was concerned with nathematical representation of the construct formed, and supposing the same conditions and notation, then "x bi'o y" is exactly the same (and the same commentary applies) except that it demands that 'R' represents '<'. (Notice additionally that, in this case, x < y must be true. However be careful to avoid reading "<" as the symbol representing "less than" in the intuitive sense for real numbers; it could just as easily be any other partial order, including the "greater than" relation).<br />
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When X does not "loop around" through the initially-potential intervals in question (it may do so through others): "bi'i" has a symmetry between its two arguments. Thus, it would be weird for conditions to be placed on exactly one of its arguments. "bi'o" is a restriction of "bi'i" which forces a directionality or order upon the line segment produced; thus "bi'o" inherits properties from "bi'i" but the broken symmetry allows conditions to be placed on any combination of its arguments in a natural context.<br />
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If X does "loop around" through at least one initially-potential interval at hand, then: "bi'i" forces the 'most natural' or 'minimal' interval to be the one which is being referenced under either ordering of the inputes, and "bi'o" results in the 'most natural' or 'minimal' interval which extends '''from''' the first argument '''to''' the second argument. For example, on a circle, where angles are measured counterclockwise (from the positive x-axis, toward the positive y-axis; an angle of measure <math>0</math> has its rays both being equivalent to the positive x-axis) and where the arguments refer to points on the circle by the angles so measured from the positive x-axis (in radians) at which they are located (modulo <math>\tau = C/r</math> for circle of circumference <math>C</math> and radius <math>r>0</math>): "<math>0</math> bi'o <math>\tau/4</math>" is equivalent to "<math>0</math> bi'i <math>\tau/4</math>" (and, therefore, "<math>\tau/4</math> bi'i <math>0</math>", which is the single arc segment which forms one quarter of the entire circle and which is between the positive x-axis and the positive y-axis; but "<math>\tau/4</math> bi'o <math>0</math>" is entirely different, being the other three quarters of the circle (and, if it matters, this is traced out via having the angle run counterclockwise from positive y-axis (at <math>\tau/4</math>) until it attains the value <math>\tau \equiv 0</math> at the positive x-axis (from 'the other side', so to speak). Throughout this article, X will typically be assumed to not 'loop around' through any initially-potential interval at hand, but the considerations made in this paragraph should apply without too much difficulty in making the analogy.<br />
* (Note that "initially-potential interval" is interpreted broadly, accounting for all conceivable references intended for the interval at hand, which means that X 'loop around' through at least one of the results of "bi'o" and of "se bi'o" for the given arguments (in fixed order); the set of such potential intervals are those which could be meant prior to the audience actually thinking too deeply about the meaning/structure (it is the set of all initial interpretations which are conceivable, regardless of whether they are possible). In this sense, an interval is a path from one of the arguments to the other. Consider a graph/network G of points with some edges. It might be the case that G is a tree (lacks any loops) except for, say, exactly one loop (a sequence of edge-connected nodes such that there is at least one path from at least one node to itself via the edges) which includes a proper subset of its nodes, numbering at least two (for simplicity). As long as both "bi'o" and "se bi'o" do not intersect nonemptily with any of the nodes/edges in this loop, then the loop can be 'excised' from consideration and we can take X to not loop around through any of the initially-potential intervals; in other words X would be the result of 'subtracting' the loop from G; such a subtraction would have no impact on the interval actually meant. On the other hand, if at least one of those intervals does indeed intersect nonemptily with the loop, then X must be taken to 'loop around' through at least one initially-potential interval at hand, and this potential 'looping' must be taken into account when interpreting/evaluating the meaning of the interval being specified).<br />
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Suppose that X does not loop through any initially-potential interval at hand.<br />
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It should be noted that, unless <math>x = \pm \infty</math> is defined and true in a given case, <math>\forall r \in [0, + \infty]</math>, "x mi'i r" refers to/forms a bounded interval or the whole space; no semi-infinite (that is: bounded from above/the positive side xor from below/the negative side) interval/line segment (ray) can be produced. The same is true for "bi'i" and "bi'o" if, additionally, r is finite; recall the previous commentary about symmetry of arguments and inheritance concerning these words. These proposals - where '<math>\infty</math>' now refers to any point which has a distance of <math>+ \infty</math> from the origin - will (or, at least, thus far have) not change(d) this fact. In both the current (non-proposed) functionality and the herein proposed functionality, the intervals which are produced by "bi'i" and "bi'o" can be bounded, semi-infinite (in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)), or infinite in both positive and negative directions (doubly-infinite/infinite; in any number of directions (so long as that number is a nonnegative integer less than or equal to twice the dimensionality of the space)); in the herein proposed functionality, these states can be simultaneously true, with the interval being semi-infinite in some dimensions, infinite in others, and bounded/finite in yet others (the total count of such dimensions being equal to the dimensionality of the space).<br />
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If we accept partial orders, the space X can be all sorts of creatures, including - for example - sets under the strict-containment/proper-subset relation (so that BIhI forms an interval of sets). However, more exotic meanings can be used/intended (although any partial order endowing the space would have to be ignored in context with respect to the meaning of BIhI, which is okay and implicitly possible within the description heretofore provided by the CLL). For example, intervals may just trace out (a possibly ordered/'directed') path between points in X, which may be - for example - the geography of locations on Earth, a network, or a set of sets (which may otherwise but inconsequentially for our purposes be endowed with the proper-subset order). In order to be clear: X need not have an order of any kind endowing it overall; however, if "bi'o" is used, the interval generated does have an ordered endowed on it (alone) which may or may not match the order endowing X, should such an order exist.<br />
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A final note for the sake of carefulness: "bi'o" establishes an order on a line segment such that its first argument is somehow 'less' than its second one. However, it does not necessarily/really establish a direction on the line segment in a graph theoretic sense. So, throughout this page, take mentions of directionality with a grain of salt - they may be the result of momentary carelessness.<br />
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=== SE BIhI ===<br />
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Although independent of this whole proposal, SE (specifically "se" and "re'au'e") should be able to precede BIhI. For "bi'i" itself, there would be no effect. For "se bi'o", the order of the arguments is switched so that the first argument of "se bi'o" is the greater/destination endpoint and the second argument thereof is the lesser/origin endpoint. Thus, "bi'i" is equivalent to "bi'o ja se bi'o". For "se mi'i", the order of the arguments is switched so that the first represents the radius length (in one-dimension: half of the length of the linear interval) and the second represents the center of the interval.<br />
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== Proposed Functionality ==<br />
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Any commentary in this article (excluding the 'Authors' and 'Current Functionality' sections) is meant to be taken as part of the "whole proposal". What follows are specific details which are broken into labelled sections for the sake of reference and hierarchy of application.<br />
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=== Main Proposal #1 ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; fix a basis B thereof. Let r be a nonnegative real number. Let x and y live in the same space X. Define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity. Define B = {<math>e_1, e_2, ..., e_n</math>}. Then there exists <math> x_1, x_2, ..., x_n, y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n), y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let "''R''" denote an 'ordering' relation on F or the ordered field of real numbers (as appropriate) which may be either the "less than" relation (denoted "<") or, as appropriate (determined by GAhO; generically, elliptical), the "less than or equal to" relation (denoted "<math>\leq</math>").<br />
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We let the dimensionality of our space (which is and can be inferred from the dimensionality of x and/or y, which should match) determine the nature of our intervals.<br />
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* "mi'i" is the easiest to redefine. In fact, the previous description needs no reworking, so long as we understand the space to be potentially larger than a line and loosen our notion of "interval". I propose that "x mi'i r" is defined to be/describe the n-dimensional hyperball (or, possibly, the closure thereof) which is centered on/at x and which has radius r. Notationally, it is <math>\{ z \in X: d(x,z)</math> ''R'' <math>r \}</math>.<br />
** In order to be clear: this interval is a neighborhood in the space; that is to say, it is a region of the space which is bounded by and internal to a sphere (but which may possibly include the boundary and/or exclude the center). This region is called a "ball".<br />
** I propose that we adopt additional keywords/glosses/terminology for "mi'i". "mi'i" should be given the keyword/gloss "centered interval"; it might also deserve the keyword/gloss "n-ball". The second argument (here denoted by "r") should be called the "radius" (in addition to "range"). The first argument (here denoted by "x") can remain with the sole label of "center".<br />
* "bi'i" requires a little more work. I propose that "x bi'i y" generates/describes the n-cell/n-orthotope which has opposite vertices at points x and y. This is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (x_i</math> ''R'' <math> \alpha_i </math> ''R'' <math> y_i)) \}</math>.<br />
** This is similar to the rectangle made on a computer by clicking the mouse at one endpoint and holding-with-dragging the cursor to the other endpoint. Note that there are as many ways to generate the same 'rectangle' as there are vertices on/of the 'rectangle' (where this jumber scales with dimensionality of the 'recrangle'). It need not be two-dimensional, though.<br />
** Terminology can again be updated (id est: added to). The interval should be additionally described as a "n-cell" and "n-orthotope interval"; "rectilinear interval" may additionally be considered. Both arguments (here denoted by "x" and "y" respectively) should be labelled as "endpoints". Symmetry between them should be noted in dictionary definitions.<br />
** This extended form of "bi'i" can be obtained via Cartesian products of linear intervals aligned with/generated by the basis elements. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
* "bi'o" has, to me (lai krtisfranks), no obvious extension since (for example) <math>\mathbb{R}^2</math> cannot be ordered.<br />
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_<br />
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When <math>F = \mathbb{R}</math>, 1-tuples/1-dimensional endpoints will be isomorphically mapped automatically to the corresponding real numbers. This allows for ease of use and back-compatibility.<br />
* This is done by establishing the identity/correspondence that <math>\forall (\xi) \in F, (\xi) \leftrightarrow \xi </math>. In other words, the functionality of intervals as defined outside of this whole proposal (which is for the 1-dimensional case) is extended so that endpoints "x" and "y" which are scalars are automatically mapped to (x) and (y) respectively, where the latter are now handled via the extended functionality herein proposed (as a point in (albeit one-dimensional) space and which has coordinates (well, exactly 1 coördinate)).<br />
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Notice that, now, "mi'i" and "bi'i" do not have the same "shape" except when the dimensionality involved is 0 or 1. The former is round whereas the latter is rectilinear. This is assuming Euclidean geometry. If other netrics are involved, they may appear to be the same or may actually be the same. For example, in taxicab geometry, a sphere <i>appears</i> to be a cross-polytope of the appropriate dimensionality, yet it is still a sphere (which bounds "mi'i"-intervals). In Chebyshev geometry, a sphere appears as an orthotope of the appropriate dimensionality, yet it is still a spehere (and the boundary of a "mi'i"-interval); in this case, though, it very well may be congruent to the n-cell (orthotope) that "bi'i" produces (under the proper conditions).<br />
* These distinct definitions are good (utile) and natural in theoretical mathematics.<br />
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=== Alternative #1: Line Segments Unless Specified Otherwise ===<br />
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An alternative (which lai .krtisfranks. finds perhaps even better than the previous proposal (Main Proposal #1)) is to have "bi'i" and "bi'o" always default to referencing line segments (generally: geodesics) in any space. That is, regardless of the space, these two cmavo (but not "mi'i") would 'draw' a line from their first argument to their second one.<br />
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Note: The endpoints (first and second arguments) of "bi'i" and "bi'o" will be points that are specified via multiple coördinates with respect to a basis. They are not merely scalars. They still must live in the same space (X) and thus must have the same number of coördinates. In this situation, the one-dimensional usage which is defined already outside of this whole proposal merely isomorphically maps scalars which are denoted by "x" and "y" to the their corresponding 1-dimensional point specifications "(x)" and "(y)" respectively. (Notice that, without an additional convention, these will never map to "(x,0,0,...)" and "(y,0,0,...)" respectively, despite the isomorphism that may be established. This is meant to avoid the abusive mixing of notation/spaces: there is no interval from (1,2) to 1, for example. We should always specify that the endpoints are higher-dimensional. This note about mapping 1 to (1) is meant solely for the purpose of making this extension back-compatible and natural.)<br />
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This would make the default usage automatically compatible with generalized points (see below). Additionally, line segments are generally useful in geometry of any (nontrivial) dimension, so this functionality would be utile.<br />
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This also would allow both "bi'i" and "bi'o" to be defined in any decent space (as opposed to only have "bi'i" be defined, which is the case in the aforementioned subproposal).<br />
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In this formulation, "x bi'o y" implies that x is in some sense a starting point of reference/of an imaginary journey and y is the corresponding termination point; both are 'endpoints'/terminals, so to speak. If the space does not 'loop around', then the set produced, however, is still exactly equivalent to that produced by "x bi'i y" and any coloring of the connotations is unmathematical (and, thus, should be avoided in the opinion of lai .krtisfranks.),; the latter is generally preferred.<br />
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Note: There is still no established directionality on the linear interval that is produced by "bi'o". However, as long as it does not conflict with any others, we might be able to assume an established order thereupon. "x bi'o y" does mean that "x < y" (along that line).<br />
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In this case, we use "ce'ei'oi" (followed by a number larger than 1 if we are being explicit) on either or both points x, y in the constructs "x bi'i y" and "x bi'o y" in order to produce the swept-out higher-dimensional-orthotopal "interval" that was proposed originally. See the 'Handling Generalized Points' section, following, for more details.<br />
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"mi'i" will still generalize to a higher-dimensional-ball in the space. (Its functionality, as described previously, and as extended immediately after this section, is unchanged.)<br />
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=== Proposed Extension A: "mi'i" ===<br />
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"mi'i" can be extended further. Keep the previous definitions and conditions. Now, undefine r. Let <math>r_1, r_2, ..., r_n \geq 0</math>.<br />
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Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just a formal n-tuple which has entries ordered in a corresponding manner - in other words, it isnjust a list of numbers (scalars in thebunderlying field, more specifically) with the order of presentation fixed by the basis of X and according to the utterer's intention. Notice that r does not technically change if the basis is changed; in such a situation, it may not be possible to describe the n-dimensional interval in simple terms (using only linear combinations of the entries of the new basis) at all and, in any case, the utterer would generally need to supply an entirely different list <math> r\prime </math> in order to convey the same thought.<br />
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* Then we can define "x mi'i r" as <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (d_F (x_i, \alpha_i)</math> ''R'' <math>r_i)) \}</math>. Notice that 'd' is now actually '<math>d_F</math>', id est: the metric on the field F. Here, each coordinate of a point <math>\alpha</math> is being compared to the corresponding coordinate of point x; if they are within the specified distance of one another (given by the corresponding entry in the list r), then that coordinate works out; iff all of the coordinates of the point work out, then the point belongs to the interval so described.<br />
** This extended form of "mi'i" can be obtained via Cartesian products of linear intervals. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
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This essentially returns us to the old situation wherein the interval is no longer an n-ball but an n-cell (matching "bi'i"). The side lengths vary (being <math>2 r_i</math> in length, for each side i). The lines which pass through their corresponding/respective midpoints and which are perpendicular to the corresponding hyperfaces will intersect at a single point, videlicet the first argument of "mi'i" constructs (the 'center'; more appropriately: circumcenter), which is the point from which the various perpendicular distances to the boundaries are each measured (being <math> r_i </math>, for the appropriate/corresponding i).<br />
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This definition is good for computer science, graphing, and experimental science. It is almost never used in theoretical mathematics. (Literally never in the experience of lai krtisfranks, at any rate.)<br />
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This additional proposal requires no major update, change, or addition to the glossing/keywords associated with "mi'i" in dictionary definitions, although there would be an implicit understanding of increased generality. If desired, however, "orthotopic interval with given circumcenter" or similar would do nicely.<br />
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* Additionally, we could establish the convention-by-definition that: <math>((\exists \rho \geq 0: ((\forall i \in \mathbb{N} \cap [1, n]), (r_i = \rho))) \implies </math> "x mi'i r" = "x mi'i <math>\rho</math>" <math>)</math>; but we would need a way to ensure that the audience recognizes <math>\rho</math> as an n-tuple and not just a scalar. Otherwise, utilization of this convention would be indistinguishable from the previously-mentioned case/proposal wherein the second argument as a single number constitutes the radius of an n-ball.<br />
** This complication can be overcome by mentioning "ce'ei'oi" immediately after "<math>\rho</math>"; if this is done, then we are to understand that "<math>\rho</math>" represents - in short-hand form - a formal tuple of identical entries (each being <math>\rho</math>). The elements of this tuple must never be negative.<br />
*** If the utterer explicitly defines/declares <math>\rho</math> to be such a formal tuple, then "ce'ei'oi" is not necessary, although it is also not wrong (and may in fact be helpful).<br />
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== Handling Generalized Points ==<br />
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If the input (x and y; the type of one determines the type of the other by forcing it to be the same) are generalized points (such as towns/geographic points), then they likely live in at-least-two-dimensional space, as is the case on Earth. However, with or without Alternative #1, they are being treated as distinct points (assigned real numbers isomorphically if Alternative #1 is not adopted; otherwise, they are free to be points in space). According to this proposal, it is not possible for the interpretation of an interval with these arguments to be anything except one-dimensional. But, for example, maybe we want to discuss the 'rectangular' (more on this immediately later/below) area of the globe between Olympia, Washington, U.S.A. (defined as x) and Tallahassee, Florida, U.S.A. (defined as y). (This rectangle covers much of the continental/contiguous U.S.) "x bi'i y" would, presumably, give the quickest route for a roadtrip or flight from Olympia to Tallahassee (the geodesic line segment (more on this immediately later/below)) or the reverse thereof (from the other to the one); it would not yield the 'rectangle' that we want. The word "ce'ei'oi" fixes this issue. If it is used on a generalized point (rather than a formal tuple - see immediately previous/above ("mi'i" discussion)), then it indicates that that endpoint (and, consequently, all others) is to be treated multi-dimensionally (unless the argument of "ce'ei'oi" is identically and exactly equal to 1). (In order to be clear: in "mi'i", the second argument (the tuple of "radius length(s)") is not considered to be an endpoint for this purpose - or, truly, anywhere within this proposal; it has a distinct nature and possibly typing separate from that of the first argument of "mi'i".) It is not necessary if Alternative #1 is not adopted and if the points are already defined to belong to a well-described space (of known dimensionality) or are decomposed in terms of their basis/represented as a tuple. If we do this, with the former definitions, then "x ce'ei'oi bi'i y" will suddenly indicate not the line(ar interval) between x and y, but instead the 'area between them'. (This area may be visualized thusly: Imagine a map with x and y on it, on a computer. Click on one of these points, drag the cursor to the other. In many programs, a (possibly degenerate) rectangle is swept out, usually with a dashed or dotted outline. The opposite corners of this rectangle are x and y; the remaining corners are given by one coordinate of x and the other coordinate of y, as appropriate. The space highlighted (within this rectangle) is the interval formed.)<br />
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Note that "x ce'ei'oi bi'i y" is equivalent to "x ce'ei'oi bi'i y ce'ei'oi" and to "x bi'i y ce'ei'oi". Likewise if we replace "bi'i" with "bi'o".<br />
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Note that "ce'ei'oi" has to follow the last argument of "bi'i" and "bi'o" when it is used therein and on the right/later side of BIhI and if the right/later BIhI argument is a scalar of nonnegative integer value; else, it will adopt the BIhI argument as its own (instead), unless its own argument is immediately followed by "boi".<br />
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The space in which this interval exists is determined by context. This is a problem even in the unextended (one-dimensional) version of these words in this usage: Is the unordered interval from Paris to London along the Earth's surface (geodesic) or is it a straight line through space (intersecting the Earth's surface at some points as well as the interior)? Is the (un)ordered interval, if geodesic, following the shorter segment of the great-circle connecting the two cities, or the longer one? (The same is true in and with Alternative #1 each.)<br />
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Note that in any case x and y need to live in the same space. So, if one is a generalized point, then the other must be. It makes no sense to discuss the interval from 1 to you or from Olympia to my imaginary friend. Moreover, they must have the same dimensionality; placing "ce'ei'oi" on one of them determines the nature of the other (and so is unnecessary); however, the argument of "ce'ei'oi" does need to be compatible with both x and y if present (for "bi'i" and "bi'o"; this is not the case for its being used upon the first argument of "mi'i", but is indeed the case in its being used on the second argument of "mi'i").<br />
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== Endpoint Clusivity Stati (Inclusion/Exclusion) ==<br />
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=== Notation, Background, Set-Up ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity; fix a basis B = {<math>e_1, e_2, ..., e_n</math>} thereof. Let x and y live in the same space X. Then there exists <math> x_1, x_2, ..., x_n,\; y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n),\; y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let <math>\rho,\; r_1, r_2, ..., r_n \geq 0</math>. Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just an n-tuple which has entries ordered in a corresponding manner. If n = 1, then we denote: x = (x) = (<math>x_1</math>), y = (y) = (<math>y_1</math>), r = (r) = (<math>r_1</math>).<br />
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Assume at least some of the previous proposals.<br />
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In this section, "endpoint status" (plural: "endpoint stati") and "clusivity" will refer to the options that an utterer has in specifying whether or not the boundary of the (multidimensional) interval is included xor excluded (along certain hyperplanes/manifolds). If such a boundary is included, then we call it "inclusive", "open", "soft", and "rounded" (due to the notation of using rounded brackets ("(" and ")") or an open circle ("○") in graphical/visual depictions). If such a boundary is excluded, then we call it "exclusive", "closed", "hard", and "square"/"sharp" (due to the notation of using square brackets ("[" and "]") or a closed circle ("●") in graphical/visual depictions). Fix an order '<' on the one-dimensional space(s) to at least one of which every linear interval is taken to belong; in each case of occurrence, appropriately redefine "''R''" <math>\in \{ ``<", ``\leq" \}</math> as determined by intent and context.<br />
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A bracket is a symbol which is used in order to denote a piece of the boundary of an interval. It also encodes endpoint status (id est: the clusivity of that part of the boundary). We use rightward-opening brackets for those which, in 1 dimension, bound the space from below/the negative side; these are "(", "[", and "【". "(" denotes such a boundary which is open; "[" denotes such a boundary which is closed; "【" will be used herein as a short-hand way of denoting the general such boundary which may, depending on context, be replaced with "(" and/or "["; this last is called a(n) (opening/rightward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. We use leftward-opening brackets for those which, in 1 dimension, bound the space from above/the positive side; these are ")", "]", and "】". ")" denotes such a boundary which is open; "]" denotes such a boundary which is closed; "】" will be used herein as a short-hand way of denoting the general such boundary which may be, depending on context, be replaced with ")" and/or "]"; this last is called a(n) (closing/leftward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. If it is not clear (especially with the usage of the lenticular brackets, which can assume various values depending on context and which may or may not be interdependent), brackets which pair or depend upon one another will be subscripted with the same label/index as appropriate.<br />
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The status of "【" or of "】" is which of the two options (inclusive or exclusive) it represents in a given instant/context. The status of ''R'' is which of "<" or "<math>\leq</math>" it represents in a given instant/context.<br />
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"<math>\times</math>" denotes the Cartesian product of sets. For sets A and B, <math> A \times B = \{ (a, b):\; a \in A \;\&\; b \in B \}</math>, where (a,b) is a tuple/point with coordinates (namely, in order: a, b) rather than, as the unfortunate notation may suggest, a linear interval from a to b. Note that it is ordered and not commutative. It can be made into a big/serial/iterating operator, denoted: "<math> \times_{i \in C} </math>", where i is an index and it takes every value in a set C subject to the order on C (if there is any).<br />
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Denote: <math>\mathbb{N} \cap [1, n] = \boxdot (n)</math>.<br />
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This section will use "ce'ei'oi" throughout its body. This is done for the sake of eliminating ambiguity and compatibility with all proposals (and alternatives) herein presented.<br />
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Terminology: In "x mi'i r" (for any dimension for x regardless of r) we call x the "center" and r the "radius (length)". Note that, even though it may be called "radius", r really refers to the length in a given dimension. (Radii are really line segments, not the lengths which are associated with them; we abuse terminology here for simplicity.) Any point which has distance from the center (according to the appropriate metric) in a given direction which is exactly equal to the appropriate radius length in the same direction is called an "on-sphere point", "outermost points", or "distant point" of the interval in question. The set of all on-sphere points of an interval is its "outer boundary" or "(outer/minimal enclosing) sphere". Note that "mi'i" may actually generate an n-orthotope (per Proposed Extension A) and thus may not seem or be spherical; the terminology does not vary in order to explicitly and individually account for such cases. The center of a "mi'i" interval is an element of the boundary (which is, generally, partitioned into outer and inner parts; the center is the sole element of the inner part thereof); thus, the center is an endpoint with a clusivity status.<br />
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Terminology: Each (n-1)-side of the n-orthotope produced via interval constructs will be called a "boundary-part" (these are the aforementioned hyperplanes segments); these generalize the notion of "endpoints" (in a slightly different way from how the arguments of BIhI do so) from the one-dimensional case. They may still be called "endpoints" in this article, even though they are not actually points. For a given interval, the set of all such boundary-parts thereof is the boundary of the interval. "mi'i" is taken to have a whole and indivisible outer boundary (without individual boundary-parts) when its dimensionality is greater than 1; when its dimensionality is equal to 1, the two outermost (end)points may be taken to each constitute a boundary-part of the outer boundary; there is an additional (inner) boundary-part, which is exactly the singleton set of the center point.<br />
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''''!'''' '''Important Result''': The n-orthotope formed by "x ce'ei'oi bi'i y (ce'ei'oi)" is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (x_i</math> ''R'' <math>_{-1,i} \alpha_i </math> ''R'' <math>_{1,i} y_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>, where: <math>\forall i \in \boxdot (n)</math>, the status of '【<math>_{i}</math>' is determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{-1,i}</math>' and likewise the status of '】<math>_{i}</math>' is analogously determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{1,i}</math>'.<br />
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=== Current Situation: the One-Dimensional Case ===<br />
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This section is according to (an interpretation of) the CLL.<br />
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In one dimension, we can specify the status of either endpoint of the (linear) interval via use of members of GAhO immediately next to the member of BIhI being used, on the appropriate side. For example, "li no ga'o bi'o ke'i li pa" represents the interval [0, 1). Notice that "ga'o" (which specifies an inclusive endpoint/boundary-part on the negative side) is on the leftern/first-uttered side of "bi'o" (id est: immediately preceding it) and follows "li no"; this means that the lesser endpoint (in this case, the point 0) is to be included. Likewise, "ke'i" (which specifies an exclusive endpoint/boundary-part) is on the rightern/last-uttered side of "bi'o" (id est: immediately following it) and precedes "li pa"; this means that the greater endpoint (in this case, the point 1) is to be excluded.<br />
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The exact same is true if we replace "bi'o" with "bi'i", although we will lose the implication that <math>0 \leq 1</math>.<br />
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Members of GAhO, at least in BIhI constructs, seem to be used - if at all - only adjacent to the member of BIhI itself. lai .krtisfranks. does not know if they are used in any other context or in any other way. There seems, to lai .krtisfranks, to be no recognition nor convention concerning how to interpret the absence of any explicit members of GAhO on one or both sides of BIhI. It does not seem possible, to lai .krtisfranks., for multiple members of GAhO or of BIhI to consecutively succeed one another (of the same selma'o) whilst being 'naked' (id est: with their dictionary meaning, without being quoted or deleted, without being JE- or JOI-connected, etc).<br />
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The structure of a BIhI construct is: [endpoint<sub>1</sub>] (GAhO*) BIhI* (GAhO*) [endpoint<sub>2</sub>].<br />
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=== Assumption/Proposal anent Unmentioned GAhO ===<br />
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The content of this section may count as an additional proposal. In any case, it is assumed throughout the rest of the article.<br />
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If, between an argument of BIhI and the BIhI cmavo itself, there is no explicitly mentioned member of GAhO, then one is still assumed to be present and to apply to and only to the appropriate boundary-part; the clusivity content of an implicit GAhO cmavo, such as in this case, is elliptical/unspecified/vague - it may or may not be determined by context, practicality, or intent, or it may be unimportant (thus, possibly, representative of either possibility).<br />
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For your information: "xau'u'oi" is a member of GAhO which is elliptical with respect to clusivity (status), as described immediately previously. It is proposed separate from and independent of/to this whole proposal or any of its parts. However, the two complement eachother well.<br />
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Whether implicit (as described herein) or explicitly elliptical, such an elliptical clusivity status will be denoted by lenticular brackets in linear intervals.<br />
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It does not make sense for a nontrivial interval of dimensionality at least 1 to neither include nor exclude any given boundary-part in the current framework of what is easily supported and expressible by Lojban; even mathematically and independent of the language, such a statement is true if it is restricted to the one-dimensional case (with end-'''points'''). Therefore, we must assume that one xor the other case applies. Thus, it should not be contentious that this assumption is made.<br />
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=== Proposed Extension B: GAhO with "mi'i", a simple case ===<br />
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There appears to be no prior usage of GAhO with "mi'i" except as proposed [[BPFK Section: Intervals|here]], a notion which lai .krtisfranks. separately formulated in his considerations for this article. The suggestion there is as follows:<br />
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GAhO before "mi'i" indicates the "endpoint status" of the center of the interval. "ga'o" there indicates that the center (the entire internal boundary-part) is definitely included (thereby forming a continuous/contiguous linear interval); the radius-distanced endpoints may or may not be included. "ke'i" there indicates that the center is definitely excluded (thereby forming a broken/punctured linear interval which misses only its center and possibly the radius-distanced endpoints). This usage in nondegenerate cases has no bearing on the clusivity of the radius-distanced endpoints (unless one specifies explicitly that these stati are mutually determinable).<br />
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GAhO after "mi'i" indicates the endpoint status of any point which has distance from the center exactly equal to the radius length specified. "ga'o" here indicates that all of the on-sphere points of the interval are definitely included (causing the outer boundary of the interval to be included; this is pictorially represented by a solid boundary curve). "ke'i" here indicates that all of the on-sphere points of the interval are definitely excluded (causing the outer boundary of the interval to be excluded; this is pictorially represented a dashed/dotted/broken boundary curve). Notice that every on-sphere point shares the same status as every other on-sphere point of a given interval. In nondegenerate cases, this usage has no bearing on the clusivity status of the center of the specified interval (unless one specifies explicitly that these stati are mutually determinable).<br />
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These descriptions apply for the one-dimensional case, but generalize - with little change - to arbritrary dimensionality. The only difference is that the interval generated will be a possibly-punctured line (segment), disc, ball, glome interior, or - generally - n-ball, depending on the dimensionality.<br />
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Let <math> x \in \mathbb{R}</math>. So, <math> x \leftrightarrow (x)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. These are all one-dimensional:<br />
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* "x mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ga'o mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ke'i mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
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* "x mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
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* "x ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
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* "x ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) < \rho \}</math>.<br />
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* "x ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) \leq \rho \}</math>.<br />
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* "x ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) < \rho \}</math>.<br />
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For emphasis: Even though the forms of the mathematical expressions are approximately the same (similar on first glance) to the analogous expressions for "bi'o", and despite the formal similarities in the Lojban utterances, it is important to realize that <math>\rho</math> here is '''not''' an endpoint of the linear interval. The presence of 'd' in the definition makes a world of difference.<br />
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=== Main Proposal #2 ===<br />
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Recall: dim(X) = n.<br />
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Note: In this section, it is taken to be the case that two mutually adjacent members of GAhO do not compound to form a member of GAhO* (in/as which they cannot be separated).<br />
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It would be nice to be able to specify the status of boundary-parts of higher-dimensional intervals. But there is a great deal of customizability that is available. The pair "vau'e'oi" and (its elidable terminator) "vau'o'oi" handle this.<br />
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The way that they work is as follows:<br />
# "vau'e'oi" opens a scope; this is called the "interval brackets scope" (hereby named "(the) IBS"). The IBS is closed via explicit use of "vau'o'oi", or immediately upon the utterance of any word which is not a member of selma'o GAhO*, or immediately upon the event of the number of explicitly utterred GAhO* members exceeding n. Thus, the only words which may belong within the IBS are members of GAhO* and they number at most n. Any GAhO cmavo explicitly used immediately after the nth explicitly used one in an IBS is ignored.<br />
# The IBS has n ordered slots; these are called "IBS slots" (or, here, just "slots"). Initially, no slots are filled. For each IBS slot, a single explicitly utterred member of GAhO* can fill it. Once one slot is filled, the next explicitly utterred GAhO* member fills the next available slot if possible/it is available. The first explicitly utterred GAhO* member fills the first IBS slot. Members of GAhO* do not need to be separated nor connected from one another in any way. They are Quine-quoted and treated as separate entities '''automatically'''. Thus, no explicit quotes are necessary.<br />
# If the IBS is closed 'prematurely' (id est: before n GAhO* members are explicitly utterred), then any IBS slot which is not explicitly filled at this point is taken to be filled by a vague/elliptical value.<br />
# Syntactically, the IBS result is treated as a single occurrence of GAhO*. Thus the IBS construct must be adjacent to an explicit member of BIhI.<br />
# Semantically/practically, the result is a formal and ordered tuple of interval brackets, the elements of which are the brackets supplied to the IBS in order such that the <math>i</math>th element of the formal tuple produced being the bracket supplied to the <math>i</math>th IBS slot. The location of this result relative to the adjacent BIhI member forces the nature of these brackets (to be rightward-opening iff the result is utterred before/is to the left of the adjacent BIhI member; to be leftward-opening iff the result is utterred after/is to the right of the adjacent BIhI member). Denote this result to be <math>(</math>''B''<math>_1, ...,</math>''B''<math>_n)</math>. Notice that this usage of the character "B" is not the same as elsewhere in this article (where it, for example, may have meant a particar basis); here, it is an individual bracket with a defined clusivity status. The role of this bracket is determined by the location of its IBS with respect to the relevant BIhI; its particular realization with respect to that boundary - that is, its applicability to one or more boundary-parts in that boundary - is determined by the slot which it fills and the basis determined by context.<br />
# The <math>i</math>th member of this tuple (namely, ''B''<math>_i</math>) acts as the corresponding bracket (opening or closing, open or closed) for the <math>i</math>th (component-)interval (parallel to the <math>i</math>th basis element) in the Cartesian product reëxpression/decomposition of the overall interval if such is possible. In other words, the clusivity of the ith hyperplane is that of the bracket B<sub>i</sub>. The order is important and corresponds via index.<br />
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Reiterating: An IBS of n > 0 slots that is closed while having only m slots explicitly filled by GAhO*, where 0 < m < n and m is an integer, has the last n-m slots filled implicitly by an elliptical GAhO* element (with restrictions intuitively/implicitly placed upon it due to context). Notice that GAhO cmavo connected by JE or JOI, for example, form a single element of GAhO* for the purpose of filling slots. There is no separator between filled slots; the GAhO* elements may just be rattled off, separated automatically and filling the slots successively.<br />
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* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> ce'ei'oi (<math>n</math>) vau'e'oi 【<math>_{1}</math> 【<math>_{2}</math> ... 【<math>_{n}</math> (vau'o'oi) bi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(y_1, y_2, ..., y_n)</math> (ce'ei'oi (<math>n</math>))", where <math>(x_1, x_2, ..., x_n)</math> and <math>(y_1, y_2, ..., y_n)</math> are expressed with respect to the basis of the space.<br />
**Notice the lack of commas/separators between brackets. Also note that only one occurrence of "ce'ei'oi" is necessary in this case (since we are working with "bi'i"). The usage of "vau'o'oi" here (in both cases) is optional.<br />
** Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (\alpha_i \in </math>【<math>_i\; x_i,\; y_i </math>】<math>_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>.<br />
*** Thus, we see that the <math>i</math>th opening bracket goes with <math>x_i</math> and the <math>i</math>th closing bracket goes with <math>y_i</math>.<br />
*** Even though it has the same generic form as was expressed in the final part of the previous "Current Functionality" subsection, the meaning is rather different. There, the brackets were elliptical/vague/generic/general. Here, they are specified by the utterrer to be whatsoever was said in the IBS.<br />
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* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> ce'ei'oi (ci) vau'e'oi ga'o ke'i ga'o (vau'o'oi) bi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(y_1, y_2, y_3)</math> (ce'ei'oi (ci)).<br />
** Then <math>I = [x_1 ,\; y_1) \times (x_2 ,\; y_2) \times [x_3 ,\; y_3]</math>. This is the basically the referent of "vei <math>x_1</math> ga'o bi'i ke'i <math>y_1</math> ve'o pi'u vei <math>x_2</math> ke'i bi'i ke'i <math>y_2</math> ve'o pi'u vei <math>x_3</math> ga'o bi'i ga'o <math>y_3</math> ve'o".<br />
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Note that in the precious two examples, so order was imposed on each linear subspace of X. This can be done, mathematically. But it was done here for convenience/for the sake of having established notation in order to make sense of the meaning in a rigorous way. If such order exists on a given linear subspace of X, then all is well for that particular instance of its imposition. However, when interpreting, one must remember to "unimpose"/"unassume" such an ordering. The linear intervals are just specified by two endpoints; the endpoints themselves can be switched (especially systematically). This, however, is a reasonable and semi-canonical way to represent the linear intervals (as long as one remembers that the endpoints need no be in the specified order); it would be confusing to switch only some of them.<br />
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Moral of the story: The IBS causes the brackets that it is given to be sent off to couple with the coordinate to which they belong, in order.<br />
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Postliminarily: It is not grammatical to have naked members of GAhO uttered consecutively in a BIhI construct except when they all are in an IBS (as enclosed by "vau'e'oi" and (possibly elided) "vau'o'oi").<br />
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=== Further Proposal: a Nice and Simple Case for Brackets ===<br />
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The content of this section supposes Main Proposal #2 as being accepted and applicable.<br />
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In this section, back-compatibility, utility/ease, and a simple and nice case are handled.<br />
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What if we do not want to say all of that? How do we support back-compatibility this way? What if all of the brackets submitted is a certain IBS are the same? Well, here is some more functionality: If the last case holds and if "ce'ei'oi" is mentioned so as to apply to an endpoint (rather than a radius length(s) entry), then we can dispense with the IBS altogether. In the multidimensional case, a single bracket ''B'' on a given side of "bi'i" is taken to be isomorphic with the formal ordered interval-bracket tuple (''B'', ..., ''B''), where the number of entries therein is the dimensionality of the space n. Id est: each GAhO cmavo actually constitutes an n-slot IBS such that every entry in it is, explicitly, that very same cmavo. Therefore, "vau'e'oi vau'o'oi" is equivalent to a single instance of "xau'u'oi" alone, allowing for n-dimensionality; this in particular is back-compatible with earlier claims/assumptions/proposals.<br />
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In the case of all the brackets on one side being (of) the same (status), we can just call the tuple by the name of the shared bracket (status). If we are working in an n-dimensional space and we are given only one bracket B outside of an IBS on a given side of "bi'i" explicitly, then we know that the IBS actually should should actually contain n brackets of form B (of the same status). This can work simultaneously on both sides of BIhI.<br />
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In short: "ce'ei'oi n ga'o bi'i" is equivalent to "ce'ei'oi n vau'e'oi ga'o ga'o [...] ga'o vau'o'oi bi'i", where "ga'o" is explicitly mentioned n times in the latter sentence. Analogy/substitution for other cases (such as: using "ke'i", having the brackets on the other side of the BIhI cmavo, or using another cmavo in BIhI) follows by the syntactic uniformity within selma'o.<br />
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Thus, <math>\forall x, y \in \mathbb{R}</math>, "x ga'o bi'i y" is mapped isomorphically to "x (ce'ei'oi pa) vau'e'oi ga'o (vau'o'oi) bi'i (vau'e'oi (vau'o'oi)) y". Recall, of course, that "x" here actually maps to "(x)" isomorphically too, and likewise for "y"; this detail was not shown for clarity, since parentheticals were employed in that example/string in order to represent optional utterrances, and the endpoints are definitely not optional in general.<br />
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Further: At most one naked member of GAhO which is not enclosed by an IBS xor at most one IBS may be explicitly used on a given side of BIhI; any more of either and/or the use of both together is ungrammatical.<br />
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=== Proposed Extension B' ===<br />
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This section assumes adoption of Proposed Extension B. If anything is to be done with "mi'i" (even in the 1-dimensional case) this subproposal (respectively Proposed Extension B) needs to be accepted.<br />
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In "mi'i", the first bracket never needs to be processed through an IBS. Either the center point is included or excluded, and this can be handled one-dimensionally (id est: by just using a member of GAhO on its own). Only one first bracket can be used/appear.<br />
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If "mi'i" is being used in order to produce/describe an n-ball (rather than an n-orthotope, per Proposed Extension A), then only one second (formally "closing") bracket can be used/appear, and- thus- it need not be processed through an IBS. In this case, every on-sphere point is either included xor they are all excluded; specification of this status can be handled one-dimensionally (id est: by just using a member of GAhO on its own).<br />
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Let <math> x \in X</math>. So, <math> x = (x_1, ..., x_n)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. "R" is used, as before, for an inequality relation that may be either strict or loose (the latter admits the possibility for equality). These are all n-dimensional:<br />
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* "x (ce'ei'oi (n)) mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball which may or may not include its external boundary (but whatsoever it does there, it does so to the totality thereof).<br />
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* "x (ce'ei'oi (n)) ga'o mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is an unpunctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ke'i mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a punctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
<br />
<br />
* "x (ce'ei'oi (n)) mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely united with its sphere (boundary); it would be drawn with a solid surface on the outside.<br />
* "x (ce'ei'oi (n)) mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely not united with its sphere (boundary); it would be drawn with a broken/dashed/dotted surface on the outside.<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
** This is a closed (solid) unpunctured disc/ball; it definitely includes both its center and its external boundary; it would be drawn with a solid surface on the outside and shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) < \rho \}</math>.<br />
** This is an open unpunctured disc/ball; it definitely includes its center but definitely excludes it external boundary; it would be drawn with a broken/dashed/dotted surface but with shading throughout the interior.<br />
** This is the typical definition of "ball" (or "disc" in two dimensions). It has only interior points, but it has all of them.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) \leq \rho \}</math>.<br />
** This is a punctured disc/ball which is united with its external sphere (external boundary); it definitely includes its external boundary but definitely excludes its center; it would be drawn with a solid surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) < \rho \}</math>.<br />
** This is a punctured disc/ball which excludes its external sphere (external boundary); it definitely excludes both its external boundary and its center; it would be drawn with a broken/dashed/dotted surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
** This is the typical definition of a punctured ball (disc in two dimensions). It is useful for the definition of limit points in topology.<br />
<br />
<br />
Clearly, as before, the definitions extend exceptionally easily for this interpretation of "mi'i". In the mathematics, the only formal change in the condition was replacing each "<math>\mathbb{R}</math>" with <math>X</math>. Of course, the points themselves have multiple coordinates and thus the meaning of 'd' gets slightly more complicated, but that is all under the hood (determined by the definition of 'd' and/or intuition about what would be appropriate for the space, given X itself).<br />
<br />
=== Proposed Extension C ===<br />
<br />
This section assumes adoption of Proposed Extension A and Proposed Extension B' (and thus Proposed Extension B).<br />
<br />
If working with "mi'i" where the first argument <math>x = (x_1, ..., x_n)</math> lives in n-dimensional space and if the second argument <math>r = (r_1, ..., r_n)</math> is a formal ordered tuple of n nonnegative extended-real numbers, then an n-cell is produced, in which case "vau'e'oi" and "vau'o'oi" work exactly as before (with "bi'i"). But it is important to note that the IBS can be nontrivial only on the second-argument side of "mi'i".<br />
<br />
Throughout this section, "d" still denotes a distance function on the space X.<br />
<br />
<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 mi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>(x_1, x_2, ..., x_n)</math> is expressed with respect to the basis of the space (and represents a point therein) and <math>r</math> formally corresponds via indices coordinatewise.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.<br />
** If, here, '【' = '(' here, let <math>C = \{ (x_1 , x_2 , x_3) \} </math>, id est the singleton of the central point; if, here, '【' = '[', then let <math> C = \{ \} </math>. Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in [0,\; r_i </math>】<math>_i)) \} \setminus C</math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ga'o (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3]</math>.<br />
*** Notice that, despite the inclusion status of the first argument, the leftern brackets in the Cartesian expression of this orthotope have varied clusivity status. The important thing is that the intervals are continuous (not missing their central point x<sub>i</sub>) due to the explicit presence of "ga'o" immediately before "mi'i"; the clusivity stati of the leftern bracket and of the rightern bracket in each Cartesian-productand should mutually match - and they are determined determined by the member of GAhO in the corresponding ISB slot in the ISB immediately following "mi'i".<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ke'i (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = \big( (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3] \big) \setminus (x_1 , x_2 , x_3 ) </math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = ((x_1 - r_1 ,\; x_1) \cup (x_1 ,\;x_1 + r_1)) \times ((x_2 - r_2 ,\; x_2) \cup (x_2 ,\;x_2 + r_2)) \times ([x_3 - r_3 ,\; x_3) \cup (x_3 ,\;x_3 + r_3])</math>.<br />
<br />
== Vocabulary/Semantics that have been Introduced ==<br />
<br />
Mostly, old vocabulary has been expanded in functionality.<br />
<br />
'''Old/CLL vocabulary with expanded functionality''':<br />
*mi'i - Originally, this word denotes/construct a line or line segment which was (taken to be) centered on the point specified by the first argument and which had length specified by the second argument. Main Proposal #1 allows "mi'i" to denote/construct a volume in n dimensions which is bounded by a sphere which is centered at the point specified by the first argument and which is of the radius specified by the second argument. Proposed Extension A allows "mi'i" to denote/construct a volume enclosed by an n-orthotope with axes parallel to those of the space (the basis) such that each side has a distance from the point, specified by the first argument, which is equal to the corresponding entry in the list which is specified by the second argument; if all entries in the list which is the second argument are the same, then the second argument may be represented by just that number via the use of "ce'ei'oi" (see later).<br />
*bi'i - Originally, this word denotes/constructs a line, linear ray, or line segment in one-dimensional space between two specified points (rays have one such point being infinite; lines have both being infinite). Main Proposal #1 extends the functionality so that this word denotes/constructs a volume enclosed by an n-orthotope in n-dimensional space (which may have any, all, or none of its faces/sides at infinity), such that each axis thereof is parallel to one axis of the space (defined by a single element of the basis); the two arguments of "bi'i" specify some pair of mutually opposite vertices on the n-orthotope - there coordinates with respect to the relevant basis determine the corresponding sides and are the corresponding endpoints in an expression of the generated volume by Cartesian product of one-dimensional linear intervals (which may be given by CLL/old "bi'i" itself).<br />
*bi'o - Originally, this word acted as "bi'i" does with the further assumption that the first argument is lesser/the origin and the second argument is greater/the destination. Its functionality was not really generalized in this whole proposal.<br />
*ga'o/ke'i - If every bracket in an IBS (see "vau'e'oi", later) would be explicitly specified as a single particular member of GAhO, then the whole IBS may be abbreviated to/represented by a single instance of the same unenclosed in an IBS.<br />
<br />
For all of these, if the points specified are one-dimensional, generic/geographic, or cannot be specified in terms of a tuple of coordinates (as given by the basis of the space), then they may be represented by a simple point/name (not enclosed in a tuple), which is isomorphic to a one-tuple of only that entry.<br />
<br />
<br />
'''New vocabulary''':<br />
<br />
*ce'ei'oi<br />
*vau'e'oi<br />
*vau'o'oi<br />
*IBS<br />
<br />
'''Independent vocabulary''':<br />
<br />
*xau'u'oi<br />
<br />
== Miscellany ==<br />
<br />
"mi'i" is really good for error bars in the sciences. In English, scientists often say stuff like "g is 9.85 plus-or-minus .05 meters per second per second". This is abusive. The only options for the value of g in such a case would be 9.80 m/s<sup>2</sup> or 9.90 m/s<sup>2</sup>. What they mean is that the value of g is between these two values (possibly including either of them). Following the format of the example quote, we have "mi'i" being the intention, with 9.85 functioning as the center and .05 as the radius. In describing a data set, one should make sure to say that the variable (usually dependent) ''belongs'' to this set, rather than it ''being'' this set. This variable will be the one with error bars in the graph. If a single variable is described in such a manner, the error bars graphically are parallel to only one axis: the actual value (as measured, within standard deviation/error) can shift in this direction (so long as it remains within the bars) but cannot shift in any other. If the error bars are applied to the ''point'', rather than the ''variable'' (which acts as a coordinate of the former), though, then the error bar will (under this proposal) envelop the point in a ball of the given radius; the actual value (as measured, within standard deviation/error) could thus shift in any direction within n-space so long as it remains within the provided radius of the given (measured, central) value. Adopting Proposed Extension A, each coordinate can be individually and independently assigned/associated with an error; the error bars will graphically be parallel to each axis (or will be 0); the actual value (as measured, within standard deviation/error for each measurement/variable/coordinate) can shift relative to the data point along each axis so long as it stays within the axis-appropriate radius of the data point.<br />
<br />
=== Further Ideas ===<br />
<br />
* It may be beneficial to us to figure out a system by which to generate basic shapes such a convex hulls via specification of important points (or sets of points). The current framework does not support such generalization since only two arguments of BIhI are presently allowed.<br />
<br />
* We may want a separate word for or modifier of "mi'i", here denoted by "<u>'''NTRVL'''</u>", such that: for <math>I \prime</math> being the interval generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 <u>'''NTRVL'''</u> vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>x = (x_1, x_2, ..., x_n) \in X</math> is expressed with respect to the basis of the space <math>X</math> (and represents a point therein) and <math>r = (r_1, r_2, ..., r_n)</math> formally corresponds via indices coordinatewise, then <math>I \prime = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Extended_Dimensionality_of_Interval_cmavo&diff=123220Extended Dimensionality of Interval cmavo2019-05-23T15:15:12Z<p>Krtisfranks: /* Current Functionality */ - correction/clarity</p>
<hr />
<div>{{jbocre/en}}<br />
<br />
<br />
Presently, the cmavo "mi'i", "bi'i", "bi'o" (which currently constitute all elements of selma'o BIhI) all represent/create one-dimensional intervals. However, in mathematics and even in daily life, there are many instances when higher-dimensional intervals are desired. This functionality should be supported.<br />
<br />
Rather than creating new cmavo for this task, the current cmavo (aforementioned) can simply be extended. The proposal described here will have the objective of supporting functionality for description of higher-dimensional intervals via extension only; only mathematical points are being discussed. The result should be back-compatible.<br />
<br />
== Contributors ==<br />
<br />
The following people have contributed to the writing of this article (or have provided ideas for it):<br />
*lai .krtisfranks.<br />
<br />
Where first-person personal pronouns are used, they refer to at least one of these individuals. However, they will be avoided whensoever possible (with explicit mention of the author's name when a personal opinion or insight is conveyed).<br />
<br />
== Current Functionality ==<br />
<br />
The cmavo of BIhI are nonlogical interval connectives. In mathematics (other options are available), one inputs a real number or possibly a generic endpoint, follows it by a cmavo of BIhI, and then mentions another real number or endpoint. The result is a description of a set of all points belonging to an interval. More explicitly:<br />
<br />
Let x and y be real numbers or points in geometric space, let r be a nonnegative real number. Let the space to which x and y belong be X. Further suppose that X does not "loop around" in any sense. Then:<br />
*x mi'i r: generates the interval centered on x which has range r on either side of x; in other words, this is the set of all points that have a distance to x that is less than (or possibly equal to) r. x is the midpoint of the interval, which has length 2r. Such a thing is sometimes denoted in a fashion similar to <math> \operatorname{B}_1 (x, r) </math>, where "B" is for "ball" and the subscript "1" tells the dimensionality of the space; this is also called an r neighborhood of x (sometimes denoted <math> \operatorname{nbhd} (x, r) </math>), where the space is inferred from context.<br />
*x bi'i y: generates the interval or unordered line segment with endpoints x and y; in other words, this is the set of all points between x and y (possibly including either, both, or neither of the endpoints). "y bi'i x" is completely equivalent to "x bi'i y"; there is no inherent order to the inputs nor direction to the line segment. This is the generic meaning for "between" when referring to an interval, in normal life or in mathematics; there is no notation for this notion which is both commonly understood and known to lai .krtisfranks. ; supposing an ordering on X, the closest thing would be an interval of form: <math>(\operatorname{min}(\{x,y\}), \operatorname{max}(\{x,y\})) \cup A</math>, where <math>A \subseteq \{x,y\}</math>. However, if X is a partially ordered space with order relation '<', then we may describe it thusly: let 'R' denote either '<' or its complement/negative '>'; then, if the endpoints are excluded, "x bi'i y" generates the set <math> \{ \alpha \in X: x </math> R <math> \alpha </math> R <math> y \} </math>. (Notice here that x and y may be presented in either order but for any given selection of presentation order, 'R' is fixed in meaning and present in both relations; if one order of presentation is true, then if the order is switched, then the resulting statement will mean the same thing but the meaning of 'R' will be changed to the other inequality relation. If an endpoint is to be included, this set will just be united with the singleton set of that endpoint. If X cannot be or is not partially ordered, then this present discussion about mathematical representation may be ignored; in such cases, this BIhI construction may still make sense, however - just revert to a more intuitive understanding based on the English description).<br />
*x bi'o y: generates the interval or 'directed' line segment with endpoints x and y in that order (starting from x and going to y); otherwise, it is equivalent to "bi'i". This is the typical meaning of intervals of form [x, y) and the like. Thus "y bi'o x" is backward relative to "x bi'o y". Continuing the discussion in the immediately previous point about "bi'i" which was concerned with nathematical representation of the construct formed, and supposing the same conditions and notation, then "x bi'o y" is exactly the same (and the same commentary applies) except that it demands that 'R' represents '<'. (Notice additionally that, in this case, x < y must be true. However be careful to avoid reading "<" as the symbol representing "less than" in the intuitive sense for real numbers; it could just as easily be any other partial order, including the "greater than" relation).<br />
<br />
When X does not "loop around" through the initially-potential intervals in question (it may do so through others): "bi'i" has a symmetry between its two arguments. Thus, it would be weird for conditions to be placed on exactly one of its arguments. "bi'o" is a restriction of "bi'i" which forces a directionality or order upon the line segment produced; thus "bi'o" inherits properties from "bi'i" but the broken symmetry allows conditions to be placed on any combination of its arguments in a natural context.<br />
<br />
If X does "loop around" through at least one initially-potential interval at hand, then: "bi'i" forces the 'most natural' or 'minimal' interval to be the one which is being referenced under either ordering of the inputes, and "bi'o" results in the 'most natural' or 'minimal' interval which extends '''from''' the first argument '''to''' the second argument. For example, on a circle, where angles are measured counterclockwise (from the positive x-axis, toward the positive y-axis; an angle of measure <math>0</math> has its rays both being equivalent to the positive x-axis) and where the arguments refer to points on the circle by the angles so measured from the positive x-axis (in radians) at which they are located (modulo <math>\tau = C/r</math> for circle of circumference <math>C</math> and radius <math>r>0</math>): "<math>0</math> bi'o <math>\tau/4</math>" is equivalent to "<math>0</math> bi'i <math>\tau/4</math>" (and, therefore, "<math>\tau/4</math> bi'i <math>0</math>", which is the single arc segment which forms one quarter of the entire circle and which is between the positive x-axis and the positive y-axis; but "<math>\tau/4</math> bi'o <math>0</math>" is entirely different, being the other three quarters of the circle (and, if it matters, this is traced out via having the angle run counterclockwise from positive y-axis (at <math>\tau/4</math>) until it attains the value <math>\tau \equiv 0</math> at the positive x-axis (from 'the other side', so to speak). Throughout this article, X will typically be assumed to not 'loop around' through any initially-potential interval at hand, but the considerations made in this paragraph should apply without too much difficulty in making the analogy.<br />
* (Note that "initially-potential interval" is interpreted broadly, accounting for all conceivable references intended for the interval at hand, which means that X 'loop around' through at least one of the results of "bi'o" and of "se bi'o" for the given arguments (in fixed order); the set of such potential intervals are those which could be meant prior to the audience actually thinking too deeply about the meaning/structure (it is the set of all initial interpretations which are conceivable, regardless of whether they are possible). In this sense, an interval is a path from one of the arguments to the other. Consider a graph/network G of points with some edges. It might be the case that G is a tree (lacks any loops) except for, say, exactly one loop (a sequence of edge-connected nodes such that there is at least one path from at least one node to itself via the edges) which includes a proper subset of its nodes, numbering at least two (for simplicity). As long as both "bi'o" and "se bi'o" do not intersect nonemptily with any of the nodes/edges in this loop, then the loop can be 'excised' from consideration and we can take X to not loop around through any of the initially-potential intervals; in other words X would be the result of 'subtracting' the loop from G; such a subtraction would have no impact on the interval actually meant. On the other hand, if at least one of those intervals does indeed intersect nonemptily with the loop, then X must be taken to 'loop around' through at least one initially-potential interval at hand, and this potential 'looping' must be taken into account when interpreting/evaluating the meaning of the interval being specified).<br />
<br />
Suppose that X does not loop through any initially-potential interval at hand.<br />
<br />
It should be noted that, unless <math>x = \pm \infty</math> is defined and true in a given case, <math>\forall r \in [0, + \infty]</math>, "x mi'i r" refers to/forms a bounded interval or the whole space; no semi-infinite (that is: bounded from above/the positive side xor from below/the negative side) interval/line segment (ray) can be produced. The same is true for "bi'i" and "bi'o" if, additionally, r is finite; recall the previous commentary about symmetry of arguments and inheritance concerning these words. These proposals - where '<math>\infty</math>' now refers to any point which has a distance of <math>+ \infty</math> from the origin - will (or, at least, thus far have) not change(d) this fact. In both the current (non-proposed) functionality and the herein proposed functionality, the intervals which are produced by "bi'i" and "bi'o" can be bounded, semi-infinite (in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)), or infinite in both positive and negative directions (doubly-infinite/infinite; in any number of directions (so long as that number is a nonnegative integer less than or equal to twice the dimensionality of the space)); in the herein proposed functionality, these states can be simultaneously true, with the interval being semi-infinite in some dimensions, infinite in others, and bounded/finite in yet others (the total count of such dimensions being equal to the dimensionality of the space).<br />
<br />
If we accept partial orders, the space X can be all sorts of creatures, including - for example - sets under the strict-containment/proper-subset relation (so that BIhI forms an interval of sets). However, more exotic meanings can be used/intended (although any partial order endowing the space would have to be ignored in context with respect to the meaning of BIhI, which is okay and implicitly possible within the description heretofore provided by the CLL). For example, intervals may just trace out (a possibly ordered/'directed') path between points in X, which may be - for example - the geography of locations on Earth, a network, or a set of sets (which may otherwise but inconsequentially for our purposes be endowed with the proper-subset order). In order to be clear: X need not have an order of any kind endowing it overall; however, if "bi'o" is used, the interval generated does have an ordered endowed on it (alone) which may or may not match the order endowing X, should such an order exist.<br />
<br />
A final note for the sake of carefulness: "bi'o" establishes an order on a line segment such that its first argument is somehow 'less' than its second one. However, it does not necessarily/really establish a direction on the line segment in a graph theoretic sense. So, throughout this page, take mentions of directionality with a grain of salt - they may be the result of momentary carelessness.<br />
<br />
=== SE BIhI ===<br />
<br />
Although independent of this whole proposal, SE (specifically "se" and "re'au'e") should be able to precede BIhI. For "bi'i" itself, there would be no effect. For "se bi'o", the order of the arguments is switched so that the first argument of "se bi'o" is the greater/destination endpoint and the second argument thereof is the lesser/origin endpoint. Thus, "bi'i" is equivalent to "bi'o ja se bi'o". For "se mi'i", the order of the arguments is switched so that the first represents the radius length (in one-dimension: half of the length of the linear interval) and the second represents the center of the interval.<br />
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== Proposed Functionality ==<br />
<br />
Any commentary in this article (excluding the 'Authors' and 'Current Functionality' sections) is meant to be taken as part of the "whole proposal". What follows are specific details which are broken into labelled sections for the sake of reference and hierarchy of application.<br />
<br />
=== Main Proposal #1 ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; fix a basis B thereof. Let r be a nonnegative real number. Let x and y live in the same space X. Define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity. Define B = {<math>e_1, e_2, ..., e_n</math>}. Then there exists <math> x_1, x_2, ..., x_n, y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n), y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let "''R''" denote an 'ordering' relation on F or the ordered field of real numbers (as appropriate) which may be either the "less than" relation (denoted "<") or, as appropriate (determined by GAhO; generically, elliptical), the "less than or equal to" relation (denoted "<math>\leq</math>").<br />
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We let the dimensionality of our space (which is and can be inferred from the dimensionality of x and/or y, which should match) determine the nature of our intervals.<br />
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* "mi'i" is the easiest to redefine. In fact, the previous description needs no reworking, so long as we understand the space to be potentially larger than a line and loosen our notion of "interval". I propose that "x mi'i r" is defined to be/describe the n-dimensional hyperball (or, possibly, the closure thereof) which is centered on/at x and which has radius r. Notationally, it is <math>\{ z \in X: d(x,z)</math> ''R'' <math>r \}</math>.<br />
** In order to be clear: this interval is a neighborhood in the space; that is to say, it is a region of the space which is bounded by and internal to a sphere (but which may possibly include the boundary and/or exclude the center). This region is called a "ball".<br />
** I propose that we adopt additional keywords/glosses/terminology for "mi'i". "mi'i" should be given the keyword/gloss "centered interval"; it might also deserve the keyword/gloss "n-ball". The second argument (here denoted by "r") should be called the "radius" (in addition to "range"). The first argument (here denoted by "x") can remain with the sole label of "center".<br />
* "bi'i" requires a little more work. I propose that "x bi'i y" generates/describes the n-cell/n-orthotope which has opposite vertices at points x and y. This is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (x_i</math> ''R'' <math> \alpha_i </math> ''R'' <math> y_i)) \}</math>.<br />
** This is similar to the rectangle made on a computer by clicking the mouse at one endpoint and holding-with-dragging the cursor to the other endpoint. Note that there are as many ways to generate the same 'rectangle' as there are vertices on/of the 'rectangle' (where this jumber scales with dimensionality of the 'recrangle'). It need not be two-dimensional, though.<br />
** Terminology can again be updated (id est: added to). The interval should be additionally described as a "n-cell" and "n-orthotope interval"; "rectilinear interval" may additionally be considered. Both arguments (here denoted by "x" and "y" respectively) should be labelled as "endpoints". Symmetry between them should be noted in dictionary definitions.<br />
** This extended form of "bi'i" can be obtained via Cartesian products of linear intervals aligned with/generated by the basis elements. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
* "bi'o" has, to me (lai krtisfranks), no obvious extension since (for example) <math>\mathbb{R}^2</math> cannot be ordered.<br />
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When <math>F = \mathbb{R}</math>, 1-tuples/1-dimensional endpoints will be isomorphically mapped automatically to the corresponding real numbers. This allows for ease of use and back-compatibility.<br />
* This is done by establishing the identity/correspondence that <math>\forall (\xi) \in F, (\xi) \leftrightarrow \xi </math>. In other words, the functionality of intervals as defined outside of this whole proposal (which is for the 1-dimensional case) is extended so that endpoints "x" and "y" which are scalars are automatically mapped to (x) and (y) respectively, where the latter are now handled via the extended functionality herein proposed (as a point in (albeit one-dimensional) space and which has coordinates (well, exactly 1 coördinate)).<br />
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Notice that, now, "mi'i" and "bi'i" do not have the same "shape" except when the dimensionality involved is 0 or 1. The former is round whereas the latter is rectilinear. This is assuming Euclidean geometry. If other netrics are involved, they may appear to be the same or may actually be the same. For example, in taxicab geometry, a sphere <i>appears</i> to be a cross-polytope of the appropriate dimensionality, yet it is still a sphere (which bounds "mi'i"-intervals). In Chebyshev geometry, a sphere appears as an orthotope of the appropriate dimensionality, yet it is still a spehere (and the boundary of a "mi'i"-interval); in this case, though, it very well may be congruent to the n-cell (orthotope) that "bi'i" produces (under the proper conditions).<br />
* These distinct definitions are good (utile) and natural in theoretical mathematics.<br />
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=== Alternative #1: Line Segments Unless Specified Otherwise ===<br />
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An alternative (which lai .krtisfranks. finds perhaps even better than the previous proposal (Main Proposal #1)) is to have "bi'i" and "bi'o" always default to referencing line segments (generally: geodesics) in any space. That is, regardless of the space, these two cmavo (but not "mi'i") would 'draw' a line from their first argument to their second one.<br />
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Note: The endpoints (first and second arguments) of "bi'i" and "bi'o" will be points that are specified via multiple coördinates with respect to a basis. They are not merely scalars. They still must live in the same space (X) and thus must have the same number of coördinates. In this situation, the one-dimensional usage which is defined already outside of this whole proposal merely isomorphically maps scalars which are denoted by "x" and "y" to the their corresponding 1-dimensional point specifications "(x)" and "(y)" respectively. (Notice that, without an additional convention, these will never map to "(x,0,0,...)" and "(y,0,0,...)" respectively, despite the isomorphism that may be established. This is meant to avoid the abusive mixing of notation/spaces: there is no interval from (1,2) to 1, for example. We should always specify that the endpoints are higher-dimensional. This note about mapping 1 to (1) is meant solely for the purpose of making this extension back-compatible and natural.)<br />
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This would make the default usage automatically compatible with generalized points (see below). Additionally, line segments are generally useful in geometry of any dimension.<br />
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This also would allow both "bi'i" and "bi'o" to be defined in any decent space (as opposed to only have "bi'i" be defined, which is the case in the aforementioned subproposal).<br />
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In this formulation, "x bi'o y" implies that x is in some sense a starting point of reference/of an imaginary journey and y is the corresponding termination point; both are 'endpoints'/terminals, so to speak. The set produced, however, is still exactly equivalent to that produced by "x bi'i y" and any coloring of the connotations is unmathematical (and, thus, should be avoided in the opinion of lai .krtisfranks.); the latter is generally preferred.<br />
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Note: There is still no established directionality on the linear interval that is produced by "bi'o". However, as long as it does not conflict with any others, we might be able to assume an established order thereupon. "x bi'o y" does mean that "x < y" (along that line).<br />
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In this case, we use "ce'ei'oi" (followed by a number larger than 1 if we are being explicit) on either or both points x, y in the constructs "x bi'i y" and "x bi'o y" in order to produce the swept-out higher-dimensional-orthotopal "interval" that was proposed originally.<br />
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"mi'i" will still generalize to a higher-dimensional-ball in the space. (Its functionality, as described previously, and as extended immediately after this section, is unchanged.)<br />
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=== Proposed Extension A: "mi'i" ===<br />
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"mi'i" can be extended further. Keep the previous definitions and conditions. Now, undefine r. Let <math>r_1, r_2, ..., r_n \geq 0</math>.<br />
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Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just a formal n-tuple which has entries ordered in a corresponding manner - in other words, it isnjust a list of numbers (scalars in thebunderlying field, more specifically) with the order of presentation fixed by the basis of X and according to the utterer's intention. Notice that r does not technically change if the basis is changed; in such a situation, it may not be possible to describe the n-dimensional interval in simple terms (using only linear combinations of the entries of the new basis) at all and, in any case, the utterer would generally need to supply an entirely different list <math> r\prime </math> in order to convey the same thought.<br />
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* Then we can define "x mi'i r" as <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (d_F (x_i, \alpha_i)</math> ''R'' <math>r_i)) \}</math>. Notice that 'd' is now actually '<math>d_F</math>', id est: the metric on the field F. Here, each coordinate of a point <math>\alpha</math> is being compared to the corresponding coordinate of point x; if they are within the specified distance of one another (given by the corresponding entry in the list r), then that coordinate works out; iff all of the coordinates of the point work out, then the point belongs to the interval so described.<br />
** This extended form of "mi'i" can be obtained via Cartesian products of linear intervals. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
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This essentially returns us to the old situation wherein the interval is no longer an n-ball but an n-cell (matching "bi'i"). The side lengths vary (being <math>2 r_i</math> in length, for each side i). The lines which pass through their corresponding/respective midpoints and which are perpendicular to the corresponding hyperfaces will intersect at a single point, videlicet the first argument of "mi'i" constructs (the 'center'; more appropriately: circumcenter), which is the point from which the various perpendicular distances to the boundaries are each measured (being <math> r_i </math>, for the appropriate/corresponding i).<br />
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This definition is good for computer science, graphing, and experimental science. It is almost never used in theoretical mathematics. (Literally never in the experience of lai krtisfranks, at any rate.)<br />
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This additional proposal requires no major update, change, or addition to the glossing/keywords associated with "mi'i" in dictionary definitions, although there would be an implicit understanding of increased generality. If desired, however, "orthotopic interval with given circumcenter" or similar would do nicely.<br />
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* Additionally, we could establish the convention-by-definition that: <math>((\exists \rho \geq 0: ((\forall i \in \mathbb{N} \cap [1, n]), (r_i = \rho))) \implies </math> "x mi'i r" = "x mi'i <math>\rho</math>" <math>)</math>; but we would need a way to ensure that the audience recognizes <math>\rho</math> as an n-tuple and not just a scalar. Otherwise, utilization of this convention would be indistinguishable from the previously-mentioned case/proposal wherein the second argument as a single number constitutes the radius of an n-ball.<br />
** This complication can be overcome by mentioning "ce'ei'oi" immediately after "<math>\rho</math>"; if this is done, then we are to understand that "<math>\rho</math>" represents - in short-hand form - a formal tuple of identical entries (each being <math>\rho</math>). The elements of this tuple must never be negative.<br />
*** If the utterer explicitly defines/declares <math>\rho</math> to be such a formal tuple, then "ce'ei'oi" is not necessary, although it is also not wrong (and may in fact be helpful).<br />
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== Handling Generalized Points ==<br />
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If the input (x and y; the type of one determines the type of the other by forcing it to be the same) are generalized points (such as towns/geographic points), then they likely live in at-least-two-dimensional space, as is the case on Earth. However, with or without Alternative #1, they are being treated as distinct points (assigned real numbers isomorphically if Alternative #1 is not adopted; otherwise, they are free to be points in space). According to this proposal, it is not possible for the interpretation of an interval with these arguments to be anything except one-dimensional. But, for example, maybe we want to discuss the 'rectangular' (more on this immediately later/below) area of the globe between Olympia, Washington, U.S.A. (defined as x) and Tallahassee, Florida, U.S.A. (defined as y). (This rectangle covers much of the continental/contiguous U.S.) "x bi'i y" would, presumably, give the quickest route for a roadtrip or flight from Olympia to Tallahassee (the geodesic line segment (more on this immediately later/below)) or the reverse thereof (from the other to the one); it would not yield the 'rectangle' that we want. The word "ce'ei'oi" fixes this issue. If it is used on a generalized point (rather than a formal tuple - see immediately previous/above ("mi'i" discussion)), then it indicates that that endpoint (and, consequently, all others) is to be treated multi-dimensionally (unless the argument of "ce'ei'oi" is identically and exactly equal to 1). (In order to be clear: in "mi'i", the second argument (the tuple of "radius length(s)") is not considered to be an endpoint for this purpose - or, truly, anywhere within this proposal; it has a distinct nature and possibly typing separate from that of the first argument of "mi'i".) It is not necessary if Alternative #1 is not adopted and if the points are already defined to belong to a well-described space (of known dimensionality) or are decomposed in terms of their basis/represented as a tuple. If we do this, with the former definitions, then "x ce'ei'oi bi'i y" will suddenly indicate not the line(ar interval) between x and y, but instead the 'area between them'. (This area may be visualized thusly: Imagine a map with x and y on it, on a computer. Click on one of these points, drag the cursor to the other. In many programs, a (possibly degenerate) rectangle is swept out, usually with a dashed or dotted outline. The opposite corners of this rectangle are x and y; the remaining corners are given by one coordinate of x and the other coordinate of y, as appropriate. The space highlighted (within this rectangle) is the interval formed.)<br />
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Note that "x ce'ei'oi bi'i y" is equivalent to "x ce'ei'oi bi'i y ce'ei'oi" and to "x bi'i y ce'ei'oi". Likewise if we replace "bi'i" with "bi'o".<br />
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Note that "ce'ei'oi" has to follow the last argument of "bi'i" and "bi'o" when it is used therein and on the right/later side of BIhI and if the right/later BIhI argument is a scalar of nonnegative integer value; else, it will adopt the BIhI argument as its own (instead), unless its own argument is immediately followed by "boi".<br />
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The space in which this interval exists is determined by context. This is a problem even in the unextended (one-dimensional) version of these words in this usage: Is the unordered interval from Paris to London along the Earth's surface (geodesic) or is it a straight line through space (intersecting the Earth's surface at some points as well as the interior)? Is the (un)ordered interval, if geodesic, following the shorter segment of the great-circle connecting the two cities, or the longer one? (The same is true in and with Alternative #1 each.)<br />
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Note that in any case x and y need to live in the same space. So, if one is a generalized point, then the other must be. It makes no sense to discuss the interval from 1 to you or from Olympia to my imaginary friend. Moreover, they must have the same dimensionality; placing "ce'ei'oi" on one of them determines the nature of the other (and so is unnecessary); however, the argument of "ce'ei'oi" does need to be compatible with both x and y if present (for "bi'i" and "bi'o"; this is not the case for its being used upon the first argument of "mi'i", but is indeed the case in its being used on the second argument of "mi'i").<br />
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== Endpoint Clusivity Stati (Inclusion/Exclusion) ==<br />
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=== Notation, Background, Set-Up ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity; fix a basis B = {<math>e_1, e_2, ..., e_n</math>} thereof. Let x and y live in the same space X. Then there exists <math> x_1, x_2, ..., x_n,\; y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n),\; y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let <math>\rho,\; r_1, r_2, ..., r_n \geq 0</math>. Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just an n-tuple which has entries ordered in a corresponding manner. If n = 1, then we denote: x = (x) = (<math>x_1</math>), y = (y) = (<math>y_1</math>), r = (r) = (<math>r_1</math>).<br />
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Assume at least some of the previous proposals.<br />
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In this section, "endpoint status" (plural: "endpoint stati") and "clusivity" will refer to the options that an utterer has in specifying whether or not the boundary of the (multidimensional) interval is included xor excluded (along certain hyperplanes/manifolds). If such a boundary is included, then we call it "inclusive", "open", "soft", and "rounded" (due to the notation of using rounded brackets ("(" and ")") or an open circle ("○") in graphical/visual depictions). If such a boundary is excluded, then we call it "exclusive", "closed", "hard", and "square"/"sharp" (due to the notation of using square brackets ("[" and "]") or a closed circle ("●") in graphical/visual depictions). Fix an order '<' on the one-dimensional space(s) to at least one of which every linear interval is taken to belong; in each case of occurrence, appropriately redefine "''R''" <math>\in \{ ``<", ``\leq" \}</math> as determined by intent and context.<br />
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A bracket is a symbol which is used in order to denote a piece of the boundary of an interval. It also encodes endpoint status (id est: the clusivity of that part of the boundary). We use rightward-opening brackets for those which, in 1 dimension, bound the space from below/the negative side; these are "(", "[", and "【". "(" denotes such a boundary which is open; "[" denotes such a boundary which is closed; "【" will be used herein as a short-hand way of denoting the general such boundary which may, depending on context, be replaced with "(" and/or "["; this last is called a(n) (opening/rightward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. We use leftward-opening brackets for those which, in 1 dimension, bound the space from above/the positive side; these are ")", "]", and "】". ")" denotes such a boundary which is open; "]" denotes such a boundary which is closed; "】" will be used herein as a short-hand way of denoting the general such boundary which may be, depending on context, be replaced with ")" and/or "]"; this last is called a(n) (closing/leftward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. If it is not clear (especially with the usage of the lenticular brackets, which can assume various values depending on context and which may or may not be interdependent), brackets which pair or depend upon one another will be subscripted with the same label/index as appropriate.<br />
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The status of "【" or of "】" is which of the two options (inclusive or exclusive) it represents in a given instant/context. The status of ''R'' is which of "<" or "<math>\leq</math>" it represents in a given instant/context.<br />
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"<math>\times</math>" denotes the Cartesian product of sets. For sets A and B, <math> A \times B = \{ (a, b):\; a \in A \;\&\; b \in B \}</math>, where (a,b) is a tuple/point with coordinates (namely, in order: a, b) rather than, as the unfortunate notation may suggest, a linear interval from a to b. Note that it is ordered and not commutative. It can be made into a big/serial/iterating operator, denoted: "<math> \times_{i \in C} </math>", where i is an index and it takes every value in a set C subject to the order on C (if there is any).<br />
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Denote: <math>\mathbb{N} \cap [1, n] = \boxdot (n)</math>.<br />
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This section will use "ce'ei'oi" throughout its body. This is done for the sake of eliminating ambiguity and compatibility with all proposals (and alternatives) herein presented.<br />
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Terminology: In "x mi'i r" (for any dimension for x regardless of r) we call x the "center" and r the "radius (length)". Note that, even though it may be called "radius", r really refers to the length in a given dimension. (Radii are really line segments, not the lengths which are associated with them; we abuse terminology here for simplicity.) Any point which has distance from the center (according to the appropriate metric) in a given direction which is exactly equal to the appropriate radius length in the same direction is called an "on-sphere point", "outermost points", or "distant point" of the interval in question. The set of all on-sphere points of an interval is its "outer boundary" or "(outer/minimal enclosing) sphere". Note that "mi'i" may actually generate an n-orthotope (per Proposed Extension A) and thus may not seem or be spherical; the terminology does not vary in order to explicitly and individually account for such cases. The center of a "mi'i" interval is an element of the boundary (which is, generally, partitioned into outer and inner parts; the center is the sole element of the inner part thereof); thus, the center is an endpoint with a clusivity status.<br />
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Terminology: Each (n-1)-side of the n-orthotope produced via interval constructs will be called a "boundary-part" (these are the aforementioned hyperplanes segments); these generalize the notion of "endpoints" (in a slightly different way from how the arguments of BIhI do so) from the one-dimensional case. They may still be called "endpoints" in this article, even though they are not actually points. For a given interval, the set of all such boundary-parts thereof is the boundary of the interval. "mi'i" is taken to have a whole and indivisible outer boundary (without individual boundary-parts) when its dimensionality is greater than 1; when its dimensionality is equal to 1, the two outermost (end)points may be taken to each constitute a boundary-part of the outer boundary; there is an additional (inner) boundary-part, which is exactly the singleton set of the center point.<br />
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''''!'''' '''Important Result''': The n-orthotope formed by "x ce'ei'oi bi'i y (ce'ei'oi)" is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (x_i</math> ''R'' <math>_{-1,i} \alpha_i </math> ''R'' <math>_{1,i} y_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>, where: <math>\forall i \in \boxdot (n)</math>, the status of '【<math>_{i}</math>' is determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{-1,i}</math>' and likewise the status of '】<math>_{i}</math>' is analogously determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{1,i}</math>'.<br />
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=== Current Situation: the One-Dimensional Case ===<br />
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This section is according to (an interpretation of) the CLL.<br />
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In one dimension, we can specify the status of either endpoint of the (linear) interval via use of members of GAhO immediately next to the member of BIhI being used, on the appropriate side. For example, "li no ga'o bi'o ke'i li pa" represents the interval [0, 1). Notice that "ga'o" (which specifies an inclusive endpoint/boundary-part on the negative side) is on the leftern/first-uttered side of "bi'o" (id est: immediately preceding it) and follows "li no"; this means that the lesser endpoint (in this case, the point 0) is to be included. Likewise, "ke'i" (which specifies an exclusive endpoint/boundary-part) is on the rightern/last-uttered side of "bi'o" (id est: immediately following it) and precedes "li pa"; this means that the greater endpoint (in this case, the point 1) is to be excluded.<br />
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The exact same is true if we replace "bi'o" with "bi'i", although we will lose the implication that <math>0 \leq 1</math>.<br />
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Members of GAhO, at least in BIhI constructs, seem to be used - if at all - only adjacent to the member of BIhI itself. lai .krtisfranks. does not know if they are used in any other context or in any other way. There seems, to lai .krtisfranks, to be no recognition nor convention concerning how to interpret the absence of any explicit members of GAhO on one or both sides of BIhI. It does not seem possible, to lai .krtisfranks., for multiple members of GAhO or of BIhI to consecutively succeed one another (of the same selma'o) whilst being 'naked' (id est: with their dictionary meaning, without being quoted or deleted, without being JE- or JOI-connected, etc).<br />
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The structure of a BIhI construct is: [endpoint<sub>1</sub>] (GAhO*) BIhI* (GAhO*) [endpoint<sub>2</sub>].<br />
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=== Assumption/Proposal anent Unmentioned GAhO ===<br />
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The content of this section may count as an additional proposal. In any case, it is assumed throughout the rest of the article.<br />
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If, between an argument of BIhI and the BIhI cmavo itself, there is no explicitly mentioned member of GAhO, then one is still assumed to be present and to apply to and only to the appropriate boundary-part; the clusivity content of an implicit GAhO cmavo, such as in this case, is elliptical/unspecified/vague - it may or may not be determined by context, practicality, or intent, or it may be unimportant (thus, possibly, representative of either possibility).<br />
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For your information: "xau'u'oi" is a member of GAhO which is elliptical with respect to clusivity (status), as described immediately previously. It is proposed separate from and independent of/to this whole proposal or any of its parts. However, the two complement eachother well.<br />
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Whether implicit (as described herein) or explicitly elliptical, such an elliptical clusivity status will be denoted by lenticular brackets in linear intervals.<br />
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It does not make sense for a nontrivial interval of dimensionality at least 1 to neither include nor exclude any given boundary-part in the current framework of what is easily supported and expressible by Lojban; even mathematically and independent of the language, such a statement is true if it is restricted to the one-dimensional case (with end-'''points'''). Therefore, we must assume that one xor the other case applies. Thus, it should not be contentious that this assumption is made.<br />
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=== Proposed Extension B: GAhO with "mi'i", a simple case ===<br />
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There appears to be no prior usage of GAhO with "mi'i" except as proposed [[BPFK Section: Intervals|here]], a notion which lai .krtisfranks. separately formulated in his considerations for this article. The suggestion there is as follows:<br />
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GAhO before "mi'i" indicates the "endpoint status" of the center of the interval. "ga'o" there indicates that the center (the entire internal boundary-part) is definitely included (thereby forming a continuous/contiguous linear interval); the radius-distanced endpoints may or may not be included. "ke'i" there indicates that the center is definitely excluded (thereby forming a broken/punctured linear interval which misses only its center and possibly the radius-distanced endpoints). This usage in nondegenerate cases has no bearing on the clusivity of the radius-distanced endpoints (unless one specifies explicitly that these stati are mutually determinable).<br />
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GAhO after "mi'i" indicates the endpoint status of any point which has distance from the center exactly equal to the radius length specified. "ga'o" here indicates that all of the on-sphere points of the interval are definitely included (causing the outer boundary of the interval to be included; this is pictorially represented by a solid boundary curve). "ke'i" here indicates that all of the on-sphere points of the interval are definitely excluded (causing the outer boundary of the interval to be excluded; this is pictorially represented a dashed/dotted/broken boundary curve). Notice that every on-sphere point shares the same status as every other on-sphere point of a given interval. In nondegenerate cases, this usage has no bearing on the clusivity status of the center of the specified interval (unless one specifies explicitly that these stati are mutually determinable).<br />
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These descriptions apply for the one-dimensional case, but generalize - with little change - to arbritrary dimensionality. The only difference is that the interval generated will be a possibly-punctured line (segment), disc, ball, glome interior, or - generally - n-ball, depending on the dimensionality.<br />
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Let <math> x \in \mathbb{R}</math>. So, <math> x \leftrightarrow (x)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. These are all one-dimensional:<br />
<br />
* "x mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
<br />
<br />
* "x ga'o mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
<br />
* "x ke'i mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
<br />
<br />
* "x mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
<br />
* "x mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
<br />
<br />
* "x ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
<br />
* "x ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) < \rho \}</math>.<br />
<br />
* "x ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) \leq \rho \}</math>.<br />
<br />
* "x ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) < \rho \}</math>.<br />
<br />
<br />
_<br />
<br />
For emphasis: Even though the forms of the mathematical expressions are approximately the same (similar on first glance) to the analogous expressions for "bi'o", and despite the formal similarities in the Lojban utterances, it is important to realize that <math>\rho</math> here is '''not''' an endpoint of the linear interval. The presence of 'd' in the definition makes a world of difference.<br />
<br />
=== Main Proposal #2 ===<br />
<br />
Recall: dim(X) = n.<br />
<br />
Note: In this section, it is taken to be the case that two mutually adjacent members of GAhO do not compound to form a member of GAhO* (in/as which they cannot be separated).<br />
<br />
<br />
<br />
<br />
It would be nice to be able to specify the status of boundary-parts of higher-dimensional intervals. But there is a great deal of customizability that is available. The pair "vau'e'oi" and (its elidable terminator) "vau'o'oi" handle this.<br />
<br />
The way that they work is as follows:<br />
# "vau'e'oi" opens a scope; this is called the "interval brackets scope" (hereby named "(the) IBS"). The IBS is closed via explicit use of "vau'o'oi", or immediately upon the utterance of any word which is not a member of selma'o GAhO*, or immediately upon the event of the number of explicitly utterred GAhO* members exceeding n. Thus, the only words which may belong within the IBS are members of GAhO* and they number at most n. Any GAhO cmavo explicitly used immediately after the nth explicitly used one in an IBS is ignored.<br />
# The IBS has n ordered slots; these are called "IBS slots" (or, here, just "slots"). Initially, no slots are filled. For each IBS slot, a single explicitly utterred member of GAhO* can fill it. Once one slot is filled, the next explicitly utterred GAhO* member fills the next available slot if possible/it is available. The first explicitly utterred GAhO* member fills the first IBS slot. Members of GAhO* do not need to be separated nor connected from one another in any way. They are Quine-quoted and treated as separate entities '''automatically'''. Thus, no explicit quotes are necessary.<br />
# If the IBS is closed 'prematurely' (id est: before n GAhO* members are explicitly utterred), then any IBS slot which is not explicitly filled at this point is taken to be filled by a vague/elliptical value.<br />
# Syntactically, the IBS result is treated as a single occurrence of GAhO*. Thus the IBS construct must be adjacent to an explicit member of BIhI.<br />
# Semantically/practically, the result is a formal and ordered tuple of interval brackets, the elements of which are the brackets supplied to the IBS in order such that the <math>i</math>th element of the formal tuple produced being the bracket supplied to the <math>i</math>th IBS slot. The location of this result relative to the adjacent BIhI member forces the nature of these brackets (to be rightward-opening iff the result is utterred before/is to the left of the adjacent BIhI member; to be leftward-opening iff the result is utterred after/is to the right of the adjacent BIhI member). Denote this result to be <math>(</math>''B''<math>_1, ...,</math>''B''<math>_n)</math>. Notice that this usage of the character "B" is not the same as elsewhere in this article (where it, for example, may have meant a particar basis); here, it is an individual bracket with a defined clusivity status. The role of this bracket is determined by the location of its IBS with respect to the relevant BIhI; its particular realization with respect to that boundary - that is, its applicability to one or more boundary-parts in that boundary - is determined by the slot which it fills and the basis determined by context.<br />
# The <math>i</math>th member of this tuple (namely, ''B''<math>_i</math>) acts as the corresponding bracket (opening or closing, open or closed) for the <math>i</math>th (component-)interval (parallel to the <math>i</math>th basis element) in the Cartesian product reëxpression/decomposition of the overall interval if such is possible. In other words, the clusivity of the ith hyperplane is that of the bracket B<sub>i</sub>. The order is important and corresponds via index.<br />
<br />
Reiterating: An IBS of n > 0 slots that is closed while having only m slots explicitly filled by GAhO*, where 0 < m < n and m is an integer, has the last n-m slots filled implicitly by an elliptical GAhO* element (with restrictions intuitively/implicitly placed upon it due to context). Notice that GAhO cmavo connected by JE or JOI, for example, form a single element of GAhO* for the purpose of filling slots. There is no separator between filled slots; the GAhO* elements may just be rattled off, separated automatically and filling the slots successively.<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> ce'ei'oi (<math>n</math>) vau'e'oi 【<math>_{1}</math> 【<math>_{2}</math> ... 【<math>_{n}</math> (vau'o'oi) bi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(y_1, y_2, ..., y_n)</math> (ce'ei'oi (<math>n</math>))", where <math>(x_1, x_2, ..., x_n)</math> and <math>(y_1, y_2, ..., y_n)</math> are expressed with respect to the basis of the space.<br />
**Notice the lack of commas/separators between brackets. Also note that only one occurrence of "ce'ei'oi" is necessary in this case (since we are working with "bi'i"). The usage of "vau'o'oi" here (in both cases) is optional.<br />
** Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (\alpha_i \in </math>【<math>_i\; x_i,\; y_i </math>】<math>_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>.<br />
*** Thus, we see that the <math>i</math>th opening bracket goes with <math>x_i</math> and the <math>i</math>th closing bracket goes with <math>y_i</math>.<br />
*** Even though it has the same generic form as was expressed in the final part of the previous "Current Functionality" subsection, the meaning is rather different. There, the brackets were elliptical/vague/generic/general. Here, they are specified by the utterrer to be whatsoever was said in the IBS.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> ce'ei'oi (ci) vau'e'oi ga'o ke'i ga'o (vau'o'oi) bi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(y_1, y_2, y_3)</math> (ce'ei'oi (ci)).<br />
** Then <math>I = [x_1 ,\; y_1) \times (x_2 ,\; y_2) \times [x_3 ,\; y_3]</math>. This is the basically the referent of "vei <math>x_1</math> ga'o bi'i ke'i <math>y_1</math> ve'o pi'u vei <math>x_2</math> ke'i bi'i ke'i <math>y_2</math> ve'o pi'u vei <math>x_3</math> ga'o bi'i ga'o <math>y_3</math> ve'o".<br />
<br />
Note that in the precious two examples, so order was imposed on each linear subspace of X. This can be done, mathematically. But it was done here for convenience/for the sake of having established notation in order to make sense of the meaning in a rigorous way. If such order exists on a given linear subspace of X, then all is well for that particular instance of its imposition. However, when interpreting, one must remember to "unimpose"/"unassume" such an ordering. The linear intervals are just specified by two endpoints; the endpoints themselves can be switched (especially systematically). This, however, is a reasonable and semi-canonical way to represent the linear intervals (as long as one remembers that the endpoints need no be in the specified order); it would be confusing to switch only some of them.<br />
<br />
Moral of the story: The IBS causes the brackets that it is given to be sent off to couple with the coordinate to which they belong, in order.<br />
<br />
Postliminarily: It is not grammatical to have naked members of GAhO uttered consecutively in a BIhI construct except when they all are in an IBS (as enclosed by "vau'e'oi" and (possibly elided) "vau'o'oi").<br />
<br />
=== Further Proposal: a Nice and Simple Case for Brackets ===<br />
<br />
The content of this section supposes Main Proposal #2 as being accepted and applicable.<br />
<br />
In this section, back-compatibility, utility/ease, and a simple and nice case are handled.<br />
<br />
What if we do not want to say all of that? How do we support back-compatibility this way? What if all of the brackets submitted is a certain IBS are the same? Well, here is some more functionality: If the last case holds and if "ce'ei'oi" is mentioned so as to apply to an endpoint (rather than a radius length(s) entry), then we can dispense with the IBS altogether. In the multidimensional case, a single bracket ''B'' on a given side of "bi'i" is taken to be isomorphic with the formal ordered interval-bracket tuple (''B'', ..., ''B''), where the number of entries therein is the dimensionality of the space n. Id est: each GAhO cmavo actually constitutes an n-slot IBS such that every entry in it is, explicitly, that very same cmavo. Therefore, "vau'e'oi vau'o'oi" is equivalent to a single instance of "xau'u'oi" alone, allowing for n-dimensionality; this in particular is back-compatible with earlier claims/assumptions/proposals.<br />
<br />
In the case of all the brackets on one side being (of) the same (status), we can just call the tuple by the name of the shared bracket (status). If we are working in an n-dimensional space and we are given only one bracket B outside of an IBS on a given side of "bi'i" explicitly, then we know that the IBS actually should should actually contain n brackets of form B (of the same status). This can work simultaneously on both sides of BIhI.<br />
<br />
In short: "ce'ei'oi n ga'o bi'i" is equivalent to "ce'ei'oi n vau'e'oi ga'o ga'o [...] ga'o vau'o'oi bi'i", where "ga'o" is explicitly mentioned n times in the latter sentence. Analogy/substitution for other cases (such as: using "ke'i", having the brackets on the other side of the BIhI cmavo, or using another cmavo in BIhI) follows by the syntactic uniformity within selma'o.<br />
<br />
Thus, <math>\forall x, y \in \mathbb{R}</math>, "x ga'o bi'i y" is mapped isomorphically to "x (ce'ei'oi pa) vau'e'oi ga'o (vau'o'oi) bi'i (vau'e'oi (vau'o'oi)) y". Recall, of course, that "x" here actually maps to "(x)" isomorphically too, and likewise for "y"; this detail was not shown for clarity, since parentheticals were employed in that example/string in order to represent optional utterrances, and the endpoints are definitely not optional in general.<br />
<br />
Further: At most one naked member of GAhO which is not enclosed by an IBS xor at most one IBS may be explicitly used on a given side of BIhI; any more of either and/or the use of both together is ungrammatical.<br />
<br />
=== Proposed Extension B' ===<br />
<br />
This section assumes adoption of Proposed Extension B. If anything is to be done with "mi'i" (even in the 1-dimensional case) this subproposal (respectively Proposed Extension B) needs to be accepted.<br />
<br />
In "mi'i", the first bracket never needs to be processed through an IBS. Either the center point is included or excluded, and this can be handled one-dimensionally (id est: by just using a member of GAhO on its own). Only one first bracket can be used/appear.<br />
<br />
If "mi'i" is being used in order to produce/describe an n-ball (rather than an n-orthotope, per Proposed Extension A), then only one second (formally "closing") bracket can be used/appear, and- thus- it need not be processed through an IBS. In this case, every on-sphere point is either included xor they are all excluded; specification of this status can be handled one-dimensionally (id est: by just using a member of GAhO on its own).<br />
<br />
<br />
<br />
Let <math> x \in X</math>. So, <math> x = (x_1, ..., x_n)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. "R" is used, as before, for an inequality relation that may be either strict or loose (the latter admits the possibility for equality). These are all n-dimensional:<br />
<br />
* "x (ce'ei'oi (n)) mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball which may or may not include its external boundary (but whatsoever it does there, it does so to the totality thereof).<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is an unpunctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ke'i mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a punctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
<br />
<br />
* "x (ce'ei'oi (n)) mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely united with its sphere (boundary); it would be drawn with a solid surface on the outside.<br />
* "x (ce'ei'oi (n)) mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely not united with its sphere (boundary); it would be drawn with a broken/dashed/dotted surface on the outside.<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
** This is a closed (solid) unpunctured disc/ball; it definitely includes both its center and its external boundary; it would be drawn with a solid surface on the outside and shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) < \rho \}</math>.<br />
** This is an open unpunctured disc/ball; it definitely includes its center but definitely excludes it external boundary; it would be drawn with a broken/dashed/dotted surface but with shading throughout the interior.<br />
** This is the typical definition of "ball" (or "disc" in two dimensions). It has only interior points, but it has all of them.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) \leq \rho \}</math>.<br />
** This is a punctured disc/ball which is united with its external sphere (external boundary); it definitely includes its external boundary but definitely excludes its center; it would be drawn with a solid surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) < \rho \}</math>.<br />
** This is a punctured disc/ball which excludes its external sphere (external boundary); it definitely excludes both its external boundary and its center; it would be drawn with a broken/dashed/dotted surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
** This is the typical definition of a punctured ball (disc in two dimensions). It is useful for the definition of limit points in topology.<br />
<br />
<br />
Clearly, as before, the definitions extend exceptionally easily for this interpretation of "mi'i". In the mathematics, the only formal change in the condition was replacing each "<math>\mathbb{R}</math>" with <math>X</math>. Of course, the points themselves have multiple coordinates and thus the meaning of 'd' gets slightly more complicated, but that is all under the hood (determined by the definition of 'd' and/or intuition about what would be appropriate for the space, given X itself).<br />
<br />
=== Proposed Extension C ===<br />
<br />
This section assumes adoption of Proposed Extension A and Proposed Extension B' (and thus Proposed Extension B).<br />
<br />
If working with "mi'i" where the first argument <math>x = (x_1, ..., x_n)</math> lives in n-dimensional space and if the second argument <math>r = (r_1, ..., r_n)</math> is a formal ordered tuple of n nonnegative extended-real numbers, then an n-cell is produced, in which case "vau'e'oi" and "vau'o'oi" work exactly as before (with "bi'i"). But it is important to note that the IBS can be nontrivial only on the second-argument side of "mi'i".<br />
<br />
Throughout this section, "d" still denotes a distance function on the space X.<br />
<br />
<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 mi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>(x_1, x_2, ..., x_n)</math> is expressed with respect to the basis of the space (and represents a point therein) and <math>r</math> formally corresponds via indices coordinatewise.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.<br />
** If, here, '【' = '(' here, let <math>C = \{ (x_1 , x_2 , x_3) \} </math>, id est the singleton of the central point; if, here, '【' = '[', then let <math> C = \{ \} </math>. Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in [0,\; r_i </math>】<math>_i)) \} \setminus C</math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ga'o (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3]</math>.<br />
*** Notice that, despite the inclusion status of the first argument, the leftern brackets in the Cartesian expression of this orthotope have varied clusivity status. The important thing is that the intervals are continuous (not missing their central point x<sub>i</sub>) due to the explicit presence of "ga'o" immediately before "mi'i"; the clusivity stati of the leftern bracket and of the rightern bracket in each Cartesian-productand should mutually match - and they are determined determined by the member of GAhO in the corresponding ISB slot in the ISB immediately following "mi'i".<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ke'i (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = \big( (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3] \big) \setminus (x_1 , x_2 , x_3 ) </math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = ((x_1 - r_1 ,\; x_1) \cup (x_1 ,\;x_1 + r_1)) \times ((x_2 - r_2 ,\; x_2) \cup (x_2 ,\;x_2 + r_2)) \times ([x_3 - r_3 ,\; x_3) \cup (x_3 ,\;x_3 + r_3])</math>.<br />
<br />
== Vocabulary/Semantics that have been Introduced ==<br />
<br />
Mostly, old vocabulary has been expanded in functionality.<br />
<br />
'''Old/CLL vocabulary with expanded functionality''':<br />
*mi'i - Originally, this word denotes/construct a line or line segment which was (taken to be) centered on the point specified by the first argument and which had length specified by the second argument. Main Proposal #1 allows "mi'i" to denote/construct a volume in n dimensions which is bounded by a sphere which is centered at the point specified by the first argument and which is of the radius specified by the second argument. Proposed Extension A allows "mi'i" to denote/construct a volume enclosed by an n-orthotope with axes parallel to those of the space (the basis) such that each side has a distance from the point, specified by the first argument, which is equal to the corresponding entry in the list which is specified by the second argument; if all entries in the list which is the second argument are the same, then the second argument may be represented by just that number via the use of "ce'ei'oi" (see later).<br />
*bi'i - Originally, this word denotes/constructs a line, linear ray, or line segment in one-dimensional space between two specified points (rays have one such point being infinite; lines have both being infinite). Main Proposal #1 extends the functionality so that this word denotes/constructs a volume enclosed by an n-orthotope in n-dimensional space (which may have any, all, or none of its faces/sides at infinity), such that each axis thereof is parallel to one axis of the space (defined by a single element of the basis); the two arguments of "bi'i" specify some pair of mutually opposite vertices on the n-orthotope - there coordinates with respect to the relevant basis determine the corresponding sides and are the corresponding endpoints in an expression of the generated volume by Cartesian product of one-dimensional linear intervals (which may be given by CLL/old "bi'i" itself).<br />
*bi'o - Originally, this word acted as "bi'i" does with the further assumption that the first argument is lesser/the origin and the second argument is greater/the destination. Its functionality was not really generalized in this whole proposal.<br />
*ga'o/ke'i - If every bracket in an IBS (see "vau'e'oi", later) would be explicitly specified as a single particular member of GAhO, then the whole IBS may be abbreviated to/represented by a single instance of the same unenclosed in an IBS.<br />
<br />
For all of these, if the points specified are one-dimensional, generic/geographic, or cannot be specified in terms of a tuple of coordinates (as given by the basis of the space), then they may be represented by a simple point/name (not enclosed in a tuple), which is isomorphic to a one-tuple of only that entry.<br />
<br />
<br />
'''New vocabulary''':<br />
<br />
*ce'ei'oi<br />
*vau'e'oi<br />
*vau'o'oi<br />
*IBS<br />
<br />
'''Independent vocabulary''':<br />
<br />
*xau'u'oi<br />
<br />
== Miscellany ==<br />
<br />
"mi'i" is really good for error bars in the sciences. In English, scientists often say stuff like "g is 9.85 plus-or-minus .05 meters per second per second". This is abusive. The only options for the value of g in such a case would be 9.80 m/s<sup>2</sup> or 9.90 m/s<sup>2</sup>. What they mean is that the value of g is between these two values (possibly including either of them). Following the format of the example quote, we have "mi'i" being the intention, with 9.85 functioning as the center and .05 as the radius. In describing a data set, one should make sure to say that the variable (usually dependent) ''belongs'' to this set, rather than it ''being'' this set. This variable will be the one with error bars in the graph. If a single variable is described in such a manner, the error bars graphically are parallel to only one axis: the actual value (as measured, within standard deviation/error) can shift in this direction (so long as it remains within the bars) but cannot shift in any other. If the error bars are applied to the ''point'', rather than the ''variable'' (which acts as a coordinate of the former), though, then the error bar will (under this proposal) envelop the point in a ball of the given radius; the actual value (as measured, within standard deviation/error) could thus shift in any direction within n-space so long as it remains within the provided radius of the given (measured, central) value. Adopting Proposed Extension A, each coordinate can be individually and independently assigned/associated with an error; the error bars will graphically be parallel to each axis (or will be 0); the actual value (as measured, within standard deviation/error for each measurement/variable/coordinate) can shift relative to the data point along each axis so long as it stays within the axis-appropriate radius of the data point.<br />
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=== Further Ideas ===<br />
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* It may be beneficial to us to figure out a system by which to generate basic shapes such a convex hulls via specification of important points (or sets of points). The current framework does not support such generalization since only two arguments of BIhI are presently allowed.<br />
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* We may want a separate word for or modifier of "mi'i", here denoted by "<u>'''NTRVL'''</u>", such that: for <math>I \prime</math> being the interval generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 <u>'''NTRVL'''</u> vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>x = (x_1, x_2, ..., x_n) \in X</math> is expressed with respect to the basis of the space <math>X</math> (and represents a point therein) and <math>r = (r_1, r_2, ..., r_n)</math> formally corresponds via indices coordinatewise, then <math>I \prime = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Extended_Dimensionality_of_Interval_cmavo&diff=123219Extended Dimensionality of Interval cmavo2019-05-23T15:08:29Z<p>Krtisfranks: /* Current Functionality */ - spacing</p>
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<div>{{jbocre/en}}<br />
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Presently, the cmavo "mi'i", "bi'i", "bi'o" (which currently constitute all elements of selma'o BIhI) all represent/create one-dimensional intervals. However, in mathematics and even in daily life, there are many instances when higher-dimensional intervals are desired. This functionality should be supported.<br />
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Rather than creating new cmavo for this task, the current cmavo (aforementioned) can simply be extended. The proposal described here will have the objective of supporting functionality for description of higher-dimensional intervals via extension only; only mathematical points are being discussed. The result should be back-compatible.<br />
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== Contributors ==<br />
<br />
The following people have contributed to the writing of this article (or have provided ideas for it):<br />
*lai .krtisfranks.<br />
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Where first-person personal pronouns are used, they refer to at least one of these individuals. However, they will be avoided whensoever possible (with explicit mention of the author's name when a personal opinion or insight is conveyed).<br />
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== Current Functionality ==<br />
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The cmavo of BIhI are nonlogical interval connectives. In mathematics (other options are available), one inputs a real number or possibly a generic endpoint, follows it by a cmavo of BIhI, and then mentions another real number or endpoint. The result is a description of a set of all points belonging to an interval. More explicitly:<br />
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Let x and y be real numbers or points in geometric space, let r be a nonnegative real number. Let the space to which x and y belong be X. Further suppose that X does not "loop around" in any sense. Then:<br />
*x mi'i r: generates the interval centered on x which has range r on either side of x; in other words, this is the set of all points that have a distance to x that is less than (or possibly equal to) r. x is the midpoint of the interval, which has length 2r. Such a thing is sometimes denoted in a fashion similar to <math> \operatorname{B}_1 (x, r) </math>, where "B" is for "ball" and the subscript "1" tells the dimensionality of the space; this is also called an r neighborhood of x (sometimes denoted <math> \operatorname{nbhd} (x, r) </math>), where the space is inferred from context.<br />
*x bi'i y: generates the interval or unordered line segment with endpoints x and y; in other words, this is the set of all points between x and y (possibly including either, both, or neither of the endpoints). "y bi'i x" is completely equivalent to "x bi'i y"; there is no inherent order to the inputs nor direction to the line segment. This is the generic meaning for "between" when referring to an interval, in normal life or in mathematics; there is no notation for this notion which is both commonly understood and known to lai .krtisfranks. ; supposing an ordering on X, the closest thing would be an interval of form: <math>(\operatorname{min}(\{x,y\}), \operatorname{max}(\{x,y\})) \cup A</math>, where <math>A \subseteq \{x,y\}</math>. However, if X is a partially ordered space with order relation '<', then we may describe it thusly: let 'R' denote either '<' or its complement/negative '>'; then, if the endpoints are excluded, "x bi'i y" generates the set <math> \{ \alpha \in X: x </math> R <math> \alpha </math> R <math> y \} </math>. (Notice here that x and y may be presented in either order but for any given selection of presentation order, 'R' is fixed in meaning and present in both relations; if one order of presentation is true, then if the order is switched, then the resulting statement will mean the same thing but the meaning of 'R' will be changed to the other inequality relation. If an endpoint is to be included, this set will just be united with the singleton set of that endpoint. If X cannot be or is not partially ordered, then this present discussion about mathematical representation may be ignored; in such cases, this BIhI construction may still make sense, however - just revert to a more intuitive understanding based on the English description).<br />
*x bi'o y: generates the interval or 'directed' line segment with endpoints x and y in that order (starting from x and going to y); otherwise, it is equivalent to "bi'i". This is the typical meaning of intervals of form [x, y) and the like. Thus "y bi'o x" is backward relative to "x bi'o y". Continuing the discussion in the immediately previous point about "bi'i" which was concerned with nathematical representation of the construct formed, and supposing the same conditions and notation, then "x bi'o y" is exactly the same (and the same commentary applies) except that it demands that 'R' represents '<'. (Notice additionally that, in this case, x < y must be true. However be careful to avoid reading "<" as the symbol representing "less than" in the intuitive sense for real numbers; it could just as easily be any other partial order, including the "greater than" relation).<br />
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When X does not "loop around" through the initially-potential intervals in question (it may do so through others): "bi'i" has a symmetry between its two arguments. Thus, it would be weird for conditions to be placed on exactly one of its arguments. "bi'o" is a restriction of "bi'i" which forces a directionality or order upon the line segment produced; thus "bi'o" inherits properties from "bi'i" but the broken symmetry allows conditions to be placed on any combination of its arguments in a natural context.<br />
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If X does "loop around" through at least one initially-potential interval at hand, then: "bi'i" forces the 'most natural' or 'minimal' interval to be the one which is being referenced under either ordering of the inputes, and "bi'o" results in the 'most natural' or 'minimal' interval which extends '''from''' the first argument '''to''' the second argument. For example, on a circle, where angles are measured counterclockwise (from the positive x-axis, toward the positive y-axis; an angle of measure <math>0</math> has its rays both being equivalent to the positive x-axis) and where the arguments refer to points on the circle by the angles so measured from the positive x-axis (in radians) at which they are located (modulo <math>\tau = C/r</math> for circle of circumference <math>C</math> and radius <math>r>0</math>): "<math>0</math> bi'o <math>\tau/4</math>" is equivalent to "<math>0</math> bi'i <math>\tau/4</math>" (and, therefore, "<math>\tau/4</math> bi'i <math>0</math>", which is the single arc segment which forms one quarter of the entire circle and which is between the positive x-axis and the positive y-axis; but "<math>\tau/4</math> bi'o <math>0</math>" is entirely different, being the other three quarters of the circle (and, if it matters, this is traced out via having the angle run counterclockwise from positive y-axis (at <math>\tau/4</math>) until it attains the value <math>\tau \equiv 0</math> at the positive x-axis (from 'the other side', so to speak). Throughout this article, X will typically be assumed to not 'loop around' through any initially-potential interval at hand, but the considerations made in this paragraph should apply without too much difficulty in making the analogy.<br />
* (Note that "initially-potential interval" is interpreted broadly, accounting for all conceivable references intended for the interval at hand, which means that X 'loop around' through at least one of the results of "bi'o" and of "se bi'o" for the given arguments (in fixed order); the set of such potential intervals are those which could be meant prior to the audience actually thinking too deeply about the meaning/structure (it is the set of all initial interpretations which are conceivable, regardless of whether they are possible). In this sense, an interval is a path from one of the arguments to the other. Consider a graph/network G of points with some edges. It might be the case that G is a tree (lacks any loops) except for, say, exactly one loop (a sequence of edge-connected nodes such that there is at least one path from at least one node to itself via the edges) which includes a proper subset of its nodes, numbering at least two (for simplicity). As long as both "bi'o" and "se bi'o" do not intersect nonemptily with any of the nodes/edges in this loop, then the loop can be 'excised' from consideration and we can take X to not loop around through any of the initially-potential intervals; in other words X would be the result of 'subtracting' the loop from G; such a subtraction would have no impact on the interval actually meant. On the other hand, if at least one of those intervals does indeed intersect nonemptily with the loop, then X must be taken to 'loop around' through at least one initially-potential interval at hand, and this potential 'looping' must be taken into account when interpreting/evaluating the meaning of the interval being specified).<br />
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It should be noted that, unless <math>x = \pm \infty</math> is defined and true in a given case, <math>\forall r \in [0, + \infty]</math>, "x mi'i r" refers to/forms a bounded interval or the whole space; no semi-infinite (that is: bounded from above/the positive side xor from below/the negative side) interval/line segment (ray) can be produced. The same is true for "bi'i" and "bi'o" if, additionally, r is finite; recall the previous commentary about symmetry of arguments and inheritance concerning these words. These proposals - where '<math>\infty</math>' now refers to any point which has a distance of <math>+ \infty</math> from the origin - will (or, at least, thus far have) not change(d) this fact. In both the current (non-proposed) functionality and the herein proposed functionality, the intervals which are produced by "bi'i" and "bi'o" can be bounded, semi-infinite (in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)), or infinite in both positive and negative directions (doubly-infinite/infinite; in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)).<br />
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If we accept partial orders, the space X can be all sorts of creatures, including - for example - sets under the strict-containment/proper-subset relation (so that BIhI forms an interval of sets). However, more exotic meanings can be used/intended (although any partial order endowing the space would have to be ignored in context with respect to the meaning of BIhI, which is okay and implicitly possible within the description heretofore provided by the CLL). For example, intervals may just trace out (a possibly ordered/'directed') path between points in X, which may be - for example - the geography of locations on Earth, a network, or a set of sets (which may otherwise but inconsequentially for our purposes be endowed with the proper-subset order). In order to be clear: X need not have an order of any kind endowing it overall; however, if "bi'o" is used, the interval generated does have an ordered endowed on it (alone) which may or may not match the order endowing X, should such an order exist.<br />
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A final note for the sake of carefulness: "bi'o" establishes an order on a line segment such that its first argument is somehow 'less' than its second one. However, it does not necessarily/really establish a direction on the line segment in a graph theoretic sense. So, throughout this page, take mentions of directionality with a grain of salt - they may be the result of momentary carelessness.<br />
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=== SE BIhI ===<br />
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Although independent of this whole proposal, SE (specifically "se" and "re'au'e") should be able to precede BIhI. For "bi'i" itself, there would be no effect. For "se bi'o", the order of the arguments is switched so that the first argument of "se bi'o" is the greater/destination endpoint and the second argument thereof is the lesser/origin endpoint. Thus, "bi'i" is equivalent to "bi'o ja se bi'o". For "se mi'i", the order of the arguments is switched so that the first represents the radius length (in one-dimension: half of the length of the linear interval) and the second represents the center of the interval.<br />
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== Proposed Functionality ==<br />
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Any commentary in this article (excluding the 'Authors' and 'Current Functionality' sections) is meant to be taken as part of the "whole proposal". What follows are specific details which are broken into labelled sections for the sake of reference and hierarchy of application.<br />
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=== Main Proposal #1 ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; fix a basis B thereof. Let r be a nonnegative real number. Let x and y live in the same space X. Define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity. Define B = {<math>e_1, e_2, ..., e_n</math>}. Then there exists <math> x_1, x_2, ..., x_n, y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n), y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let "''R''" denote an 'ordering' relation on F or the ordered field of real numbers (as appropriate) which may be either the "less than" relation (denoted "<") or, as appropriate (determined by GAhO; generically, elliptical), the "less than or equal to" relation (denoted "<math>\leq</math>").<br />
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We let the dimensionality of our space (which is and can be inferred from the dimensionality of x and/or y, which should match) determine the nature of our intervals.<br />
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* "mi'i" is the easiest to redefine. In fact, the previous description needs no reworking, so long as we understand the space to be potentially larger than a line and loosen our notion of "interval". I propose that "x mi'i r" is defined to be/describe the n-dimensional hyperball (or, possibly, the closure thereof) which is centered on/at x and which has radius r. Notationally, it is <math>\{ z \in X: d(x,z)</math> ''R'' <math>r \}</math>.<br />
** In order to be clear: this interval is a neighborhood in the space; that is to say, it is a region of the space which is bounded by and internal to a sphere (but which may possibly include the boundary and/or exclude the center). This region is called a "ball".<br />
** I propose that we adopt additional keywords/glosses/terminology for "mi'i". "mi'i" should be given the keyword/gloss "centered interval"; it might also deserve the keyword/gloss "n-ball". The second argument (here denoted by "r") should be called the "radius" (in addition to "range"). The first argument (here denoted by "x") can remain with the sole label of "center".<br />
* "bi'i" requires a little more work. I propose that "x bi'i y" generates/describes the n-cell/n-orthotope which has opposite vertices at points x and y. This is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (x_i</math> ''R'' <math> \alpha_i </math> ''R'' <math> y_i)) \}</math>.<br />
** This is similar to the rectangle made on a computer by clicking the mouse at one endpoint and holding-with-dragging the cursor to the other endpoint. Note that there are as many ways to generate the same 'rectangle' as there are vertices on/of the 'rectangle' (where this jumber scales with dimensionality of the 'recrangle'). It need not be two-dimensional, though.<br />
** Terminology can again be updated (id est: added to). The interval should be additionally described as a "n-cell" and "n-orthotope interval"; "rectilinear interval" may additionally be considered. Both arguments (here denoted by "x" and "y" respectively) should be labelled as "endpoints". Symmetry between them should be noted in dictionary definitions.<br />
** This extended form of "bi'i" can be obtained via Cartesian products of linear intervals aligned with/generated by the basis elements. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
* "bi'o" has, to me (lai krtisfranks), no obvious extension since (for example) <math>\mathbb{R}^2</math> cannot be ordered.<br />
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When <math>F = \mathbb{R}</math>, 1-tuples/1-dimensional endpoints will be isomorphically mapped automatically to the corresponding real numbers. This allows for ease of use and back-compatibility.<br />
* This is done by establishing the identity/correspondence that <math>\forall (\xi) \in F, (\xi) \leftrightarrow \xi </math>. In other words, the functionality of intervals as defined outside of this whole proposal (which is for the 1-dimensional case) is extended so that endpoints "x" and "y" which are scalars are automatically mapped to (x) and (y) respectively, where the latter are now handled via the extended functionality herein proposed (as a point in (albeit one-dimensional) space and which has coordinates (well, exactly 1 coördinate)).<br />
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Notice that, now, "mi'i" and "bi'i" do not have the same "shape" except when the dimensionality involved is 0 or 1. The former is round whereas the latter is rectilinear. This is assuming Euclidean geometry. If other netrics are involved, they may appear to be the same or may actually be the same. For example, in taxicab geometry, a sphere <i>appears</i> to be a cross-polytope of the appropriate dimensionality, yet it is still a sphere (which bounds "mi'i"-intervals). In Chebyshev geometry, a sphere appears as an orthotope of the appropriate dimensionality, yet it is still a spehere (and the boundary of a "mi'i"-interval); in this case, though, it very well may be congruent to the n-cell (orthotope) that "bi'i" produces (under the proper conditions).<br />
* These distinct definitions are good (utile) and natural in theoretical mathematics.<br />
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=== Alternative #1: Line Segments Unless Specified Otherwise ===<br />
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An alternative (which lai .krtisfranks. finds perhaps even better than the previous proposal (Main Proposal #1)) is to have "bi'i" and "bi'o" always default to referencing line segments (generally: geodesics) in any space. That is, regardless of the space, these two cmavo (but not "mi'i") would 'draw' a line from their first argument to their second one.<br />
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Note: The endpoints (first and second arguments) of "bi'i" and "bi'o" will be points that are specified via multiple coördinates with respect to a basis. They are not merely scalars. They still must live in the same space (X) and thus must have the same number of coördinates. In this situation, the one-dimensional usage which is defined already outside of this whole proposal merely isomorphically maps scalars which are denoted by "x" and "y" to the their corresponding 1-dimensional point specifications "(x)" and "(y)" respectively. (Notice that, without an additional convention, these will never map to "(x,0,0,...)" and "(y,0,0,...)" respectively, despite the isomorphism that may be established. This is meant to avoid the abusive mixing of notation/spaces: there is no interval from (1,2) to 1, for example. We should always specify that the endpoints are higher-dimensional. This note about mapping 1 to (1) is meant solely for the purpose of making this extension back-compatible and natural.)<br />
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This would make the default usage automatically compatible with generalized points (see below). Additionally, line segments are generally useful in geometry of any dimension.<br />
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This also would allow both "bi'i" and "bi'o" to be defined in any decent space (as opposed to only have "bi'i" be defined, which is the case in the aforementioned subproposal).<br />
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In this formulation, "x bi'o y" implies that x is in some sense a starting point of reference/of an imaginary journey and y is the corresponding termination point; both are 'endpoints'/terminals, so to speak. The set produced, however, is still exactly equivalent to that produced by "x bi'i y" and any coloring of the connotations is unmathematical (and, thus, should be avoided in the opinion of lai .krtisfranks.); the latter is generally preferred.<br />
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Note: There is still no established directionality on the linear interval that is produced by "bi'o". However, as long as it does not conflict with any others, we might be able to assume an established order thereupon. "x bi'o y" does mean that "x < y" (along that line).<br />
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In this case, we use "ce'ei'oi" (followed by a number larger than 1 if we are being explicit) on either or both points x, y in the constructs "x bi'i y" and "x bi'o y" in order to produce the swept-out higher-dimensional-orthotopal "interval" that was proposed originally.<br />
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"mi'i" will still generalize to a higher-dimensional-ball in the space. (Its functionality, as described previously, and as extended immediately after this section, is unchanged.)<br />
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=== Proposed Extension A: "mi'i" ===<br />
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"mi'i" can be extended further. Keep the previous definitions and conditions. Now, undefine r. Let <math>r_1, r_2, ..., r_n \geq 0</math>.<br />
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Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just a formal n-tuple which has entries ordered in a corresponding manner - in other words, it isnjust a list of numbers (scalars in thebunderlying field, more specifically) with the order of presentation fixed by the basis of X and according to the utterer's intention. Notice that r does not technically change if the basis is changed; in such a situation, it may not be possible to describe the n-dimensional interval in simple terms (using only linear combinations of the entries of the new basis) at all and, in any case, the utterer would generally need to supply an entirely different list <math> r\prime </math> in order to convey the same thought.<br />
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* Then we can define "x mi'i r" as <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (d_F (x_i, \alpha_i)</math> ''R'' <math>r_i)) \}</math>. Notice that 'd' is now actually '<math>d_F</math>', id est: the metric on the field F. Here, each coordinate of a point <math>\alpha</math> is being compared to the corresponding coordinate of point x; if they are within the specified distance of one another (given by the corresponding entry in the list r), then that coordinate works out; iff all of the coordinates of the point work out, then the point belongs to the interval so described.<br />
** This extended form of "mi'i" can be obtained via Cartesian products of linear intervals. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
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This essentially returns us to the old situation wherein the interval is no longer an n-ball but an n-cell (matching "bi'i"). The side lengths vary (being <math>2 r_i</math> in length, for each side i). The lines which pass through their corresponding/respective midpoints and which are perpendicular to the corresponding hyperfaces will intersect at a single point, videlicet the first argument of "mi'i" constructs (the 'center'; more appropriately: circumcenter), which is the point from which the various perpendicular distances to the boundaries are each measured (being <math> r_i </math>, for the appropriate/corresponding i).<br />
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This definition is good for computer science, graphing, and experimental science. It is almost never used in theoretical mathematics. (Literally never in the experience of lai krtisfranks, at any rate.)<br />
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This additional proposal requires no major update, change, or addition to the glossing/keywords associated with "mi'i" in dictionary definitions, although there would be an implicit understanding of increased generality. If desired, however, "orthotopic interval with given circumcenter" or similar would do nicely.<br />
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* Additionally, we could establish the convention-by-definition that: <math>((\exists \rho \geq 0: ((\forall i \in \mathbb{N} \cap [1, n]), (r_i = \rho))) \implies </math> "x mi'i r" = "x mi'i <math>\rho</math>" <math>)</math>; but we would need a way to ensure that the audience recognizes <math>\rho</math> as an n-tuple and not just a scalar. Otherwise, utilization of this convention would be indistinguishable from the previously-mentioned case/proposal wherein the second argument as a single number constitutes the radius of an n-ball.<br />
** This complication can be overcome by mentioning "ce'ei'oi" immediately after "<math>\rho</math>"; if this is done, then we are to understand that "<math>\rho</math>" represents - in short-hand form - a formal tuple of identical entries (each being <math>\rho</math>). The elements of this tuple must never be negative.<br />
*** If the utterer explicitly defines/declares <math>\rho</math> to be such a formal tuple, then "ce'ei'oi" is not necessary, although it is also not wrong (and may in fact be helpful).<br />
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== Handling Generalized Points ==<br />
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If the input (x and y; the type of one determines the type of the other by forcing it to be the same) are generalized points (such as towns/geographic points), then they likely live in at-least-two-dimensional space, as is the case on Earth. However, with or without Alternative #1, they are being treated as distinct points (assigned real numbers isomorphically if Alternative #1 is not adopted; otherwise, they are free to be points in space). According to this proposal, it is not possible for the interpretation of an interval with these arguments to be anything except one-dimensional. But, for example, maybe we want to discuss the 'rectangular' (more on this immediately later/below) area of the globe between Olympia, Washington, U.S.A. (defined as x) and Tallahassee, Florida, U.S.A. (defined as y). (This rectangle covers much of the continental/contiguous U.S.) "x bi'i y" would, presumably, give the quickest route for a roadtrip or flight from Olympia to Tallahassee (the geodesic line segment (more on this immediately later/below)) or the reverse thereof (from the other to the one); it would not yield the 'rectangle' that we want. The word "ce'ei'oi" fixes this issue. If it is used on a generalized point (rather than a formal tuple - see immediately previous/above ("mi'i" discussion)), then it indicates that that endpoint (and, consequently, all others) is to be treated multi-dimensionally (unless the argument of "ce'ei'oi" is identically and exactly equal to 1). (In order to be clear: in "mi'i", the second argument (the tuple of "radius length(s)") is not considered to be an endpoint for this purpose - or, truly, anywhere within this proposal; it has a distinct nature and possibly typing separate from that of the first argument of "mi'i".) It is not necessary if Alternative #1 is not adopted and if the points are already defined to belong to a well-described space (of known dimensionality) or are decomposed in terms of their basis/represented as a tuple. If we do this, with the former definitions, then "x ce'ei'oi bi'i y" will suddenly indicate not the line(ar interval) between x and y, but instead the 'area between them'. (This area may be visualized thusly: Imagine a map with x and y on it, on a computer. Click on one of these points, drag the cursor to the other. In many programs, a (possibly degenerate) rectangle is swept out, usually with a dashed or dotted outline. The opposite corners of this rectangle are x and y; the remaining corners are given by one coordinate of x and the other coordinate of y, as appropriate. The space highlighted (within this rectangle) is the interval formed.)<br />
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Note that "x ce'ei'oi bi'i y" is equivalent to "x ce'ei'oi bi'i y ce'ei'oi" and to "x bi'i y ce'ei'oi". Likewise if we replace "bi'i" with "bi'o".<br />
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Note that "ce'ei'oi" has to follow the last argument of "bi'i" and "bi'o" when it is used therein and on the right/later side of BIhI and if the right/later BIhI argument is a scalar of nonnegative integer value; else, it will adopt the BIhI argument as its own (instead), unless its own argument is immediately followed by "boi".<br />
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The space in which this interval exists is determined by context. This is a problem even in the unextended (one-dimensional) version of these words in this usage: Is the unordered interval from Paris to London along the Earth's surface (geodesic) or is it a straight line through space (intersecting the Earth's surface at some points as well as the interior)? Is the (un)ordered interval, if geodesic, following the shorter segment of the great-circle connecting the two cities, or the longer one? (The same is true in and with Alternative #1 each.)<br />
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Note that in any case x and y need to live in the same space. So, if one is a generalized point, then the other must be. It makes no sense to discuss the interval from 1 to you or from Olympia to my imaginary friend. Moreover, they must have the same dimensionality; placing "ce'ei'oi" on one of them determines the nature of the other (and so is unnecessary); however, the argument of "ce'ei'oi" does need to be compatible with both x and y if present (for "bi'i" and "bi'o"; this is not the case for its being used upon the first argument of "mi'i", but is indeed the case in its being used on the second argument of "mi'i").<br />
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== Endpoint Clusivity Stati (Inclusion/Exclusion) ==<br />
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=== Notation, Background, Set-Up ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity; fix a basis B = {<math>e_1, e_2, ..., e_n</math>} thereof. Let x and y live in the same space X. Then there exists <math> x_1, x_2, ..., x_n,\; y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n),\; y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let <math>\rho,\; r_1, r_2, ..., r_n \geq 0</math>. Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just an n-tuple which has entries ordered in a corresponding manner. If n = 1, then we denote: x = (x) = (<math>x_1</math>), y = (y) = (<math>y_1</math>), r = (r) = (<math>r_1</math>).<br />
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Assume at least some of the previous proposals.<br />
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In this section, "endpoint status" (plural: "endpoint stati") and "clusivity" will refer to the options that an utterer has in specifying whether or not the boundary of the (multidimensional) interval is included xor excluded (along certain hyperplanes/manifolds). If such a boundary is included, then we call it "inclusive", "open", "soft", and "rounded" (due to the notation of using rounded brackets ("(" and ")") or an open circle ("○") in graphical/visual depictions). If such a boundary is excluded, then we call it "exclusive", "closed", "hard", and "square"/"sharp" (due to the notation of using square brackets ("[" and "]") or a closed circle ("●") in graphical/visual depictions). Fix an order '<' on the one-dimensional space(s) to at least one of which every linear interval is taken to belong; in each case of occurrence, appropriately redefine "''R''" <math>\in \{ ``<", ``\leq" \}</math> as determined by intent and context.<br />
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A bracket is a symbol which is used in order to denote a piece of the boundary of an interval. It also encodes endpoint status (id est: the clusivity of that part of the boundary). We use rightward-opening brackets for those which, in 1 dimension, bound the space from below/the negative side; these are "(", "[", and "【". "(" denotes such a boundary which is open; "[" denotes such a boundary which is closed; "【" will be used herein as a short-hand way of denoting the general such boundary which may, depending on context, be replaced with "(" and/or "["; this last is called a(n) (opening/rightward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. We use leftward-opening brackets for those which, in 1 dimension, bound the space from above/the positive side; these are ")", "]", and "】". ")" denotes such a boundary which is open; "]" denotes such a boundary which is closed; "】" will be used herein as a short-hand way of denoting the general such boundary which may be, depending on context, be replaced with ")" and/or "]"; this last is called a(n) (closing/leftward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. If it is not clear (especially with the usage of the lenticular brackets, which can assume various values depending on context and which may or may not be interdependent), brackets which pair or depend upon one another will be subscripted with the same label/index as appropriate.<br />
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The status of "【" or of "】" is which of the two options (inclusive or exclusive) it represents in a given instant/context. The status of ''R'' is which of "<" or "<math>\leq</math>" it represents in a given instant/context.<br />
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"<math>\times</math>" denotes the Cartesian product of sets. For sets A and B, <math> A \times B = \{ (a, b):\; a \in A \;\&\; b \in B \}</math>, where (a,b) is a tuple/point with coordinates (namely, in order: a, b) rather than, as the unfortunate notation may suggest, a linear interval from a to b. Note that it is ordered and not commutative. It can be made into a big/serial/iterating operator, denoted: "<math> \times_{i \in C} </math>", where i is an index and it takes every value in a set C subject to the order on C (if there is any).<br />
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Denote: <math>\mathbb{N} \cap [1, n] = \boxdot (n)</math>.<br />
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This section will use "ce'ei'oi" throughout its body. This is done for the sake of eliminating ambiguity and compatibility with all proposals (and alternatives) herein presented.<br />
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Terminology: In "x mi'i r" (for any dimension for x regardless of r) we call x the "center" and r the "radius (length)". Note that, even though it may be called "radius", r really refers to the length in a given dimension. (Radii are really line segments, not the lengths which are associated with them; we abuse terminology here for simplicity.) Any point which has distance from the center (according to the appropriate metric) in a given direction which is exactly equal to the appropriate radius length in the same direction is called an "on-sphere point", "outermost points", or "distant point" of the interval in question. The set of all on-sphere points of an interval is its "outer boundary" or "(outer/minimal enclosing) sphere". Note that "mi'i" may actually generate an n-orthotope (per Proposed Extension A) and thus may not seem or be spherical; the terminology does not vary in order to explicitly and individually account for such cases. The center of a "mi'i" interval is an element of the boundary (which is, generally, partitioned into outer and inner parts; the center is the sole element of the inner part thereof); thus, the center is an endpoint with a clusivity status.<br />
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Terminology: Each (n-1)-side of the n-orthotope produced via interval constructs will be called a "boundary-part" (these are the aforementioned hyperplanes segments); these generalize the notion of "endpoints" (in a slightly different way from how the arguments of BIhI do so) from the one-dimensional case. They may still be called "endpoints" in this article, even though they are not actually points. For a given interval, the set of all such boundary-parts thereof is the boundary of the interval. "mi'i" is taken to have a whole and indivisible outer boundary (without individual boundary-parts) when its dimensionality is greater than 1; when its dimensionality is equal to 1, the two outermost (end)points may be taken to each constitute a boundary-part of the outer boundary; there is an additional (inner) boundary-part, which is exactly the singleton set of the center point.<br />
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''''!'''' '''Important Result''': The n-orthotope formed by "x ce'ei'oi bi'i y (ce'ei'oi)" is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (x_i</math> ''R'' <math>_{-1,i} \alpha_i </math> ''R'' <math>_{1,i} y_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>, where: <math>\forall i \in \boxdot (n)</math>, the status of '【<math>_{i}</math>' is determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{-1,i}</math>' and likewise the status of '】<math>_{i}</math>' is analogously determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{1,i}</math>'.<br />
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=== Current Situation: the One-Dimensional Case ===<br />
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This section is according to (an interpretation of) the CLL.<br />
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In one dimension, we can specify the status of either endpoint of the (linear) interval via use of members of GAhO immediately next to the member of BIhI being used, on the appropriate side. For example, "li no ga'o bi'o ke'i li pa" represents the interval [0, 1). Notice that "ga'o" (which specifies an inclusive endpoint/boundary-part on the negative side) is on the leftern/first-uttered side of "bi'o" (id est: immediately preceding it) and follows "li no"; this means that the lesser endpoint (in this case, the point 0) is to be included. Likewise, "ke'i" (which specifies an exclusive endpoint/boundary-part) is on the rightern/last-uttered side of "bi'o" (id est: immediately following it) and precedes "li pa"; this means that the greater endpoint (in this case, the point 1) is to be excluded.<br />
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The exact same is true if we replace "bi'o" with "bi'i", although we will lose the implication that <math>0 \leq 1</math>.<br />
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Members of GAhO, at least in BIhI constructs, seem to be used - if at all - only adjacent to the member of BIhI itself. lai .krtisfranks. does not know if they are used in any other context or in any other way. There seems, to lai .krtisfranks, to be no recognition nor convention concerning how to interpret the absence of any explicit members of GAhO on one or both sides of BIhI. It does not seem possible, to lai .krtisfranks., for multiple members of GAhO or of BIhI to consecutively succeed one another (of the same selma'o) whilst being 'naked' (id est: with their dictionary meaning, without being quoted or deleted, without being JE- or JOI-connected, etc).<br />
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The structure of a BIhI construct is: [endpoint<sub>1</sub>] (GAhO*) BIhI* (GAhO*) [endpoint<sub>2</sub>].<br />
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=== Assumption/Proposal anent Unmentioned GAhO ===<br />
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The content of this section may count as an additional proposal. In any case, it is assumed throughout the rest of the article.<br />
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If, between an argument of BIhI and the BIhI cmavo itself, there is no explicitly mentioned member of GAhO, then one is still assumed to be present and to apply to and only to the appropriate boundary-part; the clusivity content of an implicit GAhO cmavo, such as in this case, is elliptical/unspecified/vague - it may or may not be determined by context, practicality, or intent, or it may be unimportant (thus, possibly, representative of either possibility).<br />
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For your information: "xau'u'oi" is a member of GAhO which is elliptical with respect to clusivity (status), as described immediately previously. It is proposed separate from and independent of/to this whole proposal or any of its parts. However, the two complement eachother well.<br />
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Whether implicit (as described herein) or explicitly elliptical, such an elliptical clusivity status will be denoted by lenticular brackets in linear intervals.<br />
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It does not make sense for a nontrivial interval of dimensionality at least 1 to neither include nor exclude any given boundary-part in the current framework of what is easily supported and expressible by Lojban; even mathematically and independent of the language, such a statement is true if it is restricted to the one-dimensional case (with end-'''points'''). Therefore, we must assume that one xor the other case applies. Thus, it should not be contentious that this assumption is made.<br />
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=== Proposed Extension B: GAhO with "mi'i", a simple case ===<br />
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There appears to be no prior usage of GAhO with "mi'i" except as proposed [[BPFK Section: Intervals|here]], a notion which lai .krtisfranks. separately formulated in his considerations for this article. The suggestion there is as follows:<br />
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GAhO before "mi'i" indicates the "endpoint status" of the center of the interval. "ga'o" there indicates that the center (the entire internal boundary-part) is definitely included (thereby forming a continuous/contiguous linear interval); the radius-distanced endpoints may or may not be included. "ke'i" there indicates that the center is definitely excluded (thereby forming a broken/punctured linear interval which misses only its center and possibly the radius-distanced endpoints). This usage in nondegenerate cases has no bearing on the clusivity of the radius-distanced endpoints (unless one specifies explicitly that these stati are mutually determinable).<br />
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GAhO after "mi'i" indicates the endpoint status of any point which has distance from the center exactly equal to the radius length specified. "ga'o" here indicates that all of the on-sphere points of the interval are definitely included (causing the outer boundary of the interval to be included; this is pictorially represented by a solid boundary curve). "ke'i" here indicates that all of the on-sphere points of the interval are definitely excluded (causing the outer boundary of the interval to be excluded; this is pictorially represented a dashed/dotted/broken boundary curve). Notice that every on-sphere point shares the same status as every other on-sphere point of a given interval. In nondegenerate cases, this usage has no bearing on the clusivity status of the center of the specified interval (unless one specifies explicitly that these stati are mutually determinable).<br />
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These descriptions apply for the one-dimensional case, but generalize - with little change - to arbritrary dimensionality. The only difference is that the interval generated will be a possibly-punctured line (segment), disc, ball, glome interior, or - generally - n-ball, depending on the dimensionality.<br />
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Let <math> x \in \mathbb{R}</math>. So, <math> x \leftrightarrow (x)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. These are all one-dimensional:<br />
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* "x mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ga'o mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ke'i mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
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* "x mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
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* "x ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
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* "x ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) < \rho \}</math>.<br />
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* "x ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) \leq \rho \}</math>.<br />
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* "x ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) < \rho \}</math>.<br />
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_<br />
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For emphasis: Even though the forms of the mathematical expressions are approximately the same (similar on first glance) to the analogous expressions for "bi'o", and despite the formal similarities in the Lojban utterances, it is important to realize that <math>\rho</math> here is '''not''' an endpoint of the linear interval. The presence of 'd' in the definition makes a world of difference.<br />
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=== Main Proposal #2 ===<br />
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Recall: dim(X) = n.<br />
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Note: In this section, it is taken to be the case that two mutually adjacent members of GAhO do not compound to form a member of GAhO* (in/as which they cannot be separated).<br />
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It would be nice to be able to specify the status of boundary-parts of higher-dimensional intervals. But there is a great deal of customizability that is available. The pair "vau'e'oi" and (its elidable terminator) "vau'o'oi" handle this.<br />
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The way that they work is as follows:<br />
# "vau'e'oi" opens a scope; this is called the "interval brackets scope" (hereby named "(the) IBS"). The IBS is closed via explicit use of "vau'o'oi", or immediately upon the utterance of any word which is not a member of selma'o GAhO*, or immediately upon the event of the number of explicitly utterred GAhO* members exceeding n. Thus, the only words which may belong within the IBS are members of GAhO* and they number at most n. Any GAhO cmavo explicitly used immediately after the nth explicitly used one in an IBS is ignored.<br />
# The IBS has n ordered slots; these are called "IBS slots" (or, here, just "slots"). Initially, no slots are filled. For each IBS slot, a single explicitly utterred member of GAhO* can fill it. Once one slot is filled, the next explicitly utterred GAhO* member fills the next available slot if possible/it is available. The first explicitly utterred GAhO* member fills the first IBS slot. Members of GAhO* do not need to be separated nor connected from one another in any way. They are Quine-quoted and treated as separate entities '''automatically'''. Thus, no explicit quotes are necessary.<br />
# If the IBS is closed 'prematurely' (id est: before n GAhO* members are explicitly utterred), then any IBS slot which is not explicitly filled at this point is taken to be filled by a vague/elliptical value.<br />
# Syntactically, the IBS result is treated as a single occurrence of GAhO*. Thus the IBS construct must be adjacent to an explicit member of BIhI.<br />
# Semantically/practically, the result is a formal and ordered tuple of interval brackets, the elements of which are the brackets supplied to the IBS in order such that the <math>i</math>th element of the formal tuple produced being the bracket supplied to the <math>i</math>th IBS slot. The location of this result relative to the adjacent BIhI member forces the nature of these brackets (to be rightward-opening iff the result is utterred before/is to the left of the adjacent BIhI member; to be leftward-opening iff the result is utterred after/is to the right of the adjacent BIhI member). Denote this result to be <math>(</math>''B''<math>_1, ...,</math>''B''<math>_n)</math>. Notice that this usage of the character "B" is not the same as elsewhere in this article (where it, for example, may have meant a particar basis); here, it is an individual bracket with a defined clusivity status. The role of this bracket is determined by the location of its IBS with respect to the relevant BIhI; its particular realization with respect to that boundary - that is, its applicability to one or more boundary-parts in that boundary - is determined by the slot which it fills and the basis determined by context.<br />
# The <math>i</math>th member of this tuple (namely, ''B''<math>_i</math>) acts as the corresponding bracket (opening or closing, open or closed) for the <math>i</math>th (component-)interval (parallel to the <math>i</math>th basis element) in the Cartesian product reëxpression/decomposition of the overall interval if such is possible. In other words, the clusivity of the ith hyperplane is that of the bracket B<sub>i</sub>. The order is important and corresponds via index.<br />
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Reiterating: An IBS of n > 0 slots that is closed while having only m slots explicitly filled by GAhO*, where 0 < m < n and m is an integer, has the last n-m slots filled implicitly by an elliptical GAhO* element (with restrictions intuitively/implicitly placed upon it due to context). Notice that GAhO cmavo connected by JE or JOI, for example, form a single element of GAhO* for the purpose of filling slots. There is no separator between filled slots; the GAhO* elements may just be rattled off, separated automatically and filling the slots successively.<br />
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* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> ce'ei'oi (<math>n</math>) vau'e'oi 【<math>_{1}</math> 【<math>_{2}</math> ... 【<math>_{n}</math> (vau'o'oi) bi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(y_1, y_2, ..., y_n)</math> (ce'ei'oi (<math>n</math>))", where <math>(x_1, x_2, ..., x_n)</math> and <math>(y_1, y_2, ..., y_n)</math> are expressed with respect to the basis of the space.<br />
**Notice the lack of commas/separators between brackets. Also note that only one occurrence of "ce'ei'oi" is necessary in this case (since we are working with "bi'i"). The usage of "vau'o'oi" here (in both cases) is optional.<br />
** Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (\alpha_i \in </math>【<math>_i\; x_i,\; y_i </math>】<math>_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>.<br />
*** Thus, we see that the <math>i</math>th opening bracket goes with <math>x_i</math> and the <math>i</math>th closing bracket goes with <math>y_i</math>.<br />
*** Even though it has the same generic form as was expressed in the final part of the previous "Current Functionality" subsection, the meaning is rather different. There, the brackets were elliptical/vague/generic/general. Here, they are specified by the utterrer to be whatsoever was said in the IBS.<br />
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* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> ce'ei'oi (ci) vau'e'oi ga'o ke'i ga'o (vau'o'oi) bi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(y_1, y_2, y_3)</math> (ce'ei'oi (ci)).<br />
** Then <math>I = [x_1 ,\; y_1) \times (x_2 ,\; y_2) \times [x_3 ,\; y_3]</math>. This is the basically the referent of "vei <math>x_1</math> ga'o bi'i ke'i <math>y_1</math> ve'o pi'u vei <math>x_2</math> ke'i bi'i ke'i <math>y_2</math> ve'o pi'u vei <math>x_3</math> ga'o bi'i ga'o <math>y_3</math> ve'o".<br />
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Note that in the precious two examples, so order was imposed on each linear subspace of X. This can be done, mathematically. But it was done here for convenience/for the sake of having established notation in order to make sense of the meaning in a rigorous way. If such order exists on a given linear subspace of X, then all is well for that particular instance of its imposition. However, when interpreting, one must remember to "unimpose"/"unassume" such an ordering. The linear intervals are just specified by two endpoints; the endpoints themselves can be switched (especially systematically). This, however, is a reasonable and semi-canonical way to represent the linear intervals (as long as one remembers that the endpoints need no be in the specified order); it would be confusing to switch only some of them.<br />
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Moral of the story: The IBS causes the brackets that it is given to be sent off to couple with the coordinate to which they belong, in order.<br />
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Postliminarily: It is not grammatical to have naked members of GAhO uttered consecutively in a BIhI construct except when they all are in an IBS (as enclosed by "vau'e'oi" and (possibly elided) "vau'o'oi").<br />
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=== Further Proposal: a Nice and Simple Case for Brackets ===<br />
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The content of this section supposes Main Proposal #2 as being accepted and applicable.<br />
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In this section, back-compatibility, utility/ease, and a simple and nice case are handled.<br />
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What if we do not want to say all of that? How do we support back-compatibility this way? What if all of the brackets submitted is a certain IBS are the same? Well, here is some more functionality: If the last case holds and if "ce'ei'oi" is mentioned so as to apply to an endpoint (rather than a radius length(s) entry), then we can dispense with the IBS altogether. In the multidimensional case, a single bracket ''B'' on a given side of "bi'i" is taken to be isomorphic with the formal ordered interval-bracket tuple (''B'', ..., ''B''), where the number of entries therein is the dimensionality of the space n. Id est: each GAhO cmavo actually constitutes an n-slot IBS such that every entry in it is, explicitly, that very same cmavo. Therefore, "vau'e'oi vau'o'oi" is equivalent to a single instance of "xau'u'oi" alone, allowing for n-dimensionality; this in particular is back-compatible with earlier claims/assumptions/proposals.<br />
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In the case of all the brackets on one side being (of) the same (status), we can just call the tuple by the name of the shared bracket (status). If we are working in an n-dimensional space and we are given only one bracket B outside of an IBS on a given side of "bi'i" explicitly, then we know that the IBS actually should should actually contain n brackets of form B (of the same status). This can work simultaneously on both sides of BIhI.<br />
<br />
In short: "ce'ei'oi n ga'o bi'i" is equivalent to "ce'ei'oi n vau'e'oi ga'o ga'o [...] ga'o vau'o'oi bi'i", where "ga'o" is explicitly mentioned n times in the latter sentence. Analogy/substitution for other cases (such as: using "ke'i", having the brackets on the other side of the BIhI cmavo, or using another cmavo in BIhI) follows by the syntactic uniformity within selma'o.<br />
<br />
Thus, <math>\forall x, y \in \mathbb{R}</math>, "x ga'o bi'i y" is mapped isomorphically to "x (ce'ei'oi pa) vau'e'oi ga'o (vau'o'oi) bi'i (vau'e'oi (vau'o'oi)) y". Recall, of course, that "x" here actually maps to "(x)" isomorphically too, and likewise for "y"; this detail was not shown for clarity, since parentheticals were employed in that example/string in order to represent optional utterrances, and the endpoints are definitely not optional in general.<br />
<br />
Further: At most one naked member of GAhO which is not enclosed by an IBS xor at most one IBS may be explicitly used on a given side of BIhI; any more of either and/or the use of both together is ungrammatical.<br />
<br />
=== Proposed Extension B' ===<br />
<br />
This section assumes adoption of Proposed Extension B. If anything is to be done with "mi'i" (even in the 1-dimensional case) this subproposal (respectively Proposed Extension B) needs to be accepted.<br />
<br />
In "mi'i", the first bracket never needs to be processed through an IBS. Either the center point is included or excluded, and this can be handled one-dimensionally (id est: by just using a member of GAhO on its own). Only one first bracket can be used/appear.<br />
<br />
If "mi'i" is being used in order to produce/describe an n-ball (rather than an n-orthotope, per Proposed Extension A), then only one second (formally "closing") bracket can be used/appear, and- thus- it need not be processed through an IBS. In this case, every on-sphere point is either included xor they are all excluded; specification of this status can be handled one-dimensionally (id est: by just using a member of GAhO on its own).<br />
<br />
<br />
<br />
Let <math> x \in X</math>. So, <math> x = (x_1, ..., x_n)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. "R" is used, as before, for an inequality relation that may be either strict or loose (the latter admits the possibility for equality). These are all n-dimensional:<br />
<br />
* "x (ce'ei'oi (n)) mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball which may or may not include its external boundary (but whatsoever it does there, it does so to the totality thereof).<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is an unpunctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ke'i mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a punctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
<br />
<br />
* "x (ce'ei'oi (n)) mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely united with its sphere (boundary); it would be drawn with a solid surface on the outside.<br />
* "x (ce'ei'oi (n)) mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely not united with its sphere (boundary); it would be drawn with a broken/dashed/dotted surface on the outside.<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
** This is a closed (solid) unpunctured disc/ball; it definitely includes both its center and its external boundary; it would be drawn with a solid surface on the outside and shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) < \rho \}</math>.<br />
** This is an open unpunctured disc/ball; it definitely includes its center but definitely excludes it external boundary; it would be drawn with a broken/dashed/dotted surface but with shading throughout the interior.<br />
** This is the typical definition of "ball" (or "disc" in two dimensions). It has only interior points, but it has all of them.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) \leq \rho \}</math>.<br />
** This is a punctured disc/ball which is united with its external sphere (external boundary); it definitely includes its external boundary but definitely excludes its center; it would be drawn with a solid surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) < \rho \}</math>.<br />
** This is a punctured disc/ball which excludes its external sphere (external boundary); it definitely excludes both its external boundary and its center; it would be drawn with a broken/dashed/dotted surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
** This is the typical definition of a punctured ball (disc in two dimensions). It is useful for the definition of limit points in topology.<br />
<br />
<br />
Clearly, as before, the definitions extend exceptionally easily for this interpretation of "mi'i". In the mathematics, the only formal change in the condition was replacing each "<math>\mathbb{R}</math>" with <math>X</math>. Of course, the points themselves have multiple coordinates and thus the meaning of 'd' gets slightly more complicated, but that is all under the hood (determined by the definition of 'd' and/or intuition about what would be appropriate for the space, given X itself).<br />
<br />
=== Proposed Extension C ===<br />
<br />
This section assumes adoption of Proposed Extension A and Proposed Extension B' (and thus Proposed Extension B).<br />
<br />
If working with "mi'i" where the first argument <math>x = (x_1, ..., x_n)</math> lives in n-dimensional space and if the second argument <math>r = (r_1, ..., r_n)</math> is a formal ordered tuple of n nonnegative extended-real numbers, then an n-cell is produced, in which case "vau'e'oi" and "vau'o'oi" work exactly as before (with "bi'i"). But it is important to note that the IBS can be nontrivial only on the second-argument side of "mi'i".<br />
<br />
Throughout this section, "d" still denotes a distance function on the space X.<br />
<br />
<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 mi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>(x_1, x_2, ..., x_n)</math> is expressed with respect to the basis of the space (and represents a point therein) and <math>r</math> formally corresponds via indices coordinatewise.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.<br />
** If, here, '【' = '(' here, let <math>C = \{ (x_1 , x_2 , x_3) \} </math>, id est the singleton of the central point; if, here, '【' = '[', then let <math> C = \{ \} </math>. Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in [0,\; r_i </math>】<math>_i)) \} \setminus C</math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ga'o (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3]</math>.<br />
*** Notice that, despite the inclusion status of the first argument, the leftern brackets in the Cartesian expression of this orthotope have varied clusivity status. The important thing is that the intervals are continuous (not missing their central point x<sub>i</sub>) due to the explicit presence of "ga'o" immediately before "mi'i"; the clusivity stati of the leftern bracket and of the rightern bracket in each Cartesian-productand should mutually match - and they are determined determined by the member of GAhO in the corresponding ISB slot in the ISB immediately following "mi'i".<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ke'i (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = \big( (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3] \big) \setminus (x_1 , x_2 , x_3 ) </math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = ((x_1 - r_1 ,\; x_1) \cup (x_1 ,\;x_1 + r_1)) \times ((x_2 - r_2 ,\; x_2) \cup (x_2 ,\;x_2 + r_2)) \times ([x_3 - r_3 ,\; x_3) \cup (x_3 ,\;x_3 + r_3])</math>.<br />
<br />
== Vocabulary/Semantics that have been Introduced ==<br />
<br />
Mostly, old vocabulary has been expanded in functionality.<br />
<br />
'''Old/CLL vocabulary with expanded functionality''':<br />
*mi'i - Originally, this word denotes/construct a line or line segment which was (taken to be) centered on the point specified by the first argument and which had length specified by the second argument. Main Proposal #1 allows "mi'i" to denote/construct a volume in n dimensions which is bounded by a sphere which is centered at the point specified by the first argument and which is of the radius specified by the second argument. Proposed Extension A allows "mi'i" to denote/construct a volume enclosed by an n-orthotope with axes parallel to those of the space (the basis) such that each side has a distance from the point, specified by the first argument, which is equal to the corresponding entry in the list which is specified by the second argument; if all entries in the list which is the second argument are the same, then the second argument may be represented by just that number via the use of "ce'ei'oi" (see later).<br />
*bi'i - Originally, this word denotes/constructs a line, linear ray, or line segment in one-dimensional space between two specified points (rays have one such point being infinite; lines have both being infinite). Main Proposal #1 extends the functionality so that this word denotes/constructs a volume enclosed by an n-orthotope in n-dimensional space (which may have any, all, or none of its faces/sides at infinity), such that each axis thereof is parallel to one axis of the space (defined by a single element of the basis); the two arguments of "bi'i" specify some pair of mutually opposite vertices on the n-orthotope - there coordinates with respect to the relevant basis determine the corresponding sides and are the corresponding endpoints in an expression of the generated volume by Cartesian product of one-dimensional linear intervals (which may be given by CLL/old "bi'i" itself).<br />
*bi'o - Originally, this word acted as "bi'i" does with the further assumption that the first argument is lesser/the origin and the second argument is greater/the destination. Its functionality was not really generalized in this whole proposal.<br />
*ga'o/ke'i - If every bracket in an IBS (see "vau'e'oi", later) would be explicitly specified as a single particular member of GAhO, then the whole IBS may be abbreviated to/represented by a single instance of the same unenclosed in an IBS.<br />
<br />
For all of these, if the points specified are one-dimensional, generic/geographic, or cannot be specified in terms of a tuple of coordinates (as given by the basis of the space), then they may be represented by a simple point/name (not enclosed in a tuple), which is isomorphic to a one-tuple of only that entry.<br />
<br />
<br />
'''New vocabulary''':<br />
<br />
*ce'ei'oi<br />
*vau'e'oi<br />
*vau'o'oi<br />
*IBS<br />
<br />
'''Independent vocabulary''':<br />
<br />
*xau'u'oi<br />
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== Miscellany ==<br />
<br />
"mi'i" is really good for error bars in the sciences. In English, scientists often say stuff like "g is 9.85 plus-or-minus .05 meters per second per second". This is abusive. The only options for the value of g in such a case would be 9.80 m/s<sup>2</sup> or 9.90 m/s<sup>2</sup>. What they mean is that the value of g is between these two values (possibly including either of them). Following the format of the example quote, we have "mi'i" being the intention, with 9.85 functioning as the center and .05 as the radius. In describing a data set, one should make sure to say that the variable (usually dependent) ''belongs'' to this set, rather than it ''being'' this set. This variable will be the one with error bars in the graph. If a single variable is described in such a manner, the error bars graphically are parallel to only one axis: the actual value (as measured, within standard deviation/error) can shift in this direction (so long as it remains within the bars) but cannot shift in any other. If the error bars are applied to the ''point'', rather than the ''variable'' (which acts as a coordinate of the former), though, then the error bar will (under this proposal) envelop the point in a ball of the given radius; the actual value (as measured, within standard deviation/error) could thus shift in any direction within n-space so long as it remains within the provided radius of the given (measured, central) value. Adopting Proposed Extension A, each coordinate can be individually and independently assigned/associated with an error; the error bars will graphically be parallel to each axis (or will be 0); the actual value (as measured, within standard deviation/error for each measurement/variable/coordinate) can shift relative to the data point along each axis so long as it stays within the axis-appropriate radius of the data point.<br />
<br />
=== Further Ideas ===<br />
<br />
* It may be beneficial to us to figure out a system by which to generate basic shapes such a convex hulls via specification of important points (or sets of points). The current framework does not support such generalization since only two arguments of BIhI are presently allowed.<br />
<br />
* We may want a separate word for or modifier of "mi'i", here denoted by "<u>'''NTRVL'''</u>", such that: for <math>I \prime</math> being the interval generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 <u>'''NTRVL'''</u> vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>x = (x_1, x_2, ..., x_n) \in X</math> is expressed with respect to the basis of the space <math>X</math> (and represents a point therein) and <math>r = (r_1, r_2, ..., r_n)</math> formally corresponds via indices coordinatewise, then <math>I \prime = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Extended_Dimensionality_of_Interval_cmavo&diff=123218Extended Dimensionality of Interval cmavo2019-05-23T15:04:51Z<p>Krtisfranks: /* Current Functionality */ - added information</p>
<hr />
<div>{{jbocre/en}}<br />
<br />
<br />
Presently, the cmavo "mi'i", "bi'i", "bi'o" (which currently constitute all elements of selma'o BIhI) all represent/create one-dimensional intervals. However, in mathematics and even in daily life, there are many instances when higher-dimensional intervals are desired. This functionality should be supported.<br />
<br />
Rather than creating new cmavo for this task, the current cmavo (aforementioned) can simply be extended. The proposal described here will have the objective of supporting functionality for description of higher-dimensional intervals via extension only; only mathematical points are being discussed. The result should be back-compatible.<br />
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== Contributors ==<br />
<br />
The following people have contributed to the writing of this article (or have provided ideas for it):<br />
*lai .krtisfranks.<br />
<br />
Where first-person personal pronouns are used, they refer to at least one of these individuals. However, they will be avoided whensoever possible (with explicit mention of the author's name when a personal opinion or insight is conveyed).<br />
<br />
== Current Functionality ==<br />
<br />
The cmavo of BIhI are nonlogical interval connectives. In mathematics (other options are available), one inputs a real number or possibly a generic endpoint, follows it by a cmavo of BIhI, and then mentions another real number or endpoint. The result is a description of a set of all points belonging to an interval. More explicitly:<br />
Let x and y be real numbers or points in geometric space, let r be a nonnegative real number. Let the space to which x and y belong be X. Further suppose that X does not "loop around" in any sense. Then:<br />
*x mi'i r: generates the interval centered on x which has range r on either side of x; in other words, this is the set of all points that have a distance to x that is less than (or possibly equal to) r. x is the midpoint of the interval, which has length 2r. Such a thing is sometimes denoted in a fashion similar to <math> \operatorname{B}_1 (x, r) </math>, where "B" is for "ball" and the subscript "1" tells the dimensionality of the space; this is also called an r neighborhood of x (sometimes denoted <math> \operatorname{nbhd} (x, r) </math>), where the space is inferred from context.<br />
*x bi'i y: generates the interval or unordered line segment with endpoints x and y; in other words, this is the set of all points between x and y (possibly including either, both, or neither of the endpoints). "y bi'i x" is completely equivalent to "x bi'i y"; there is no inherent order to the inputs nor direction to the line segment. This is the generic meaning for "between" when referring to an interval, in normal life or in mathematics; there is no notation for this notion which is both commonly understood and known to lai .krtisfranks. ; supposing an ordering on X, the closest thing would be an interval of form: <math>(\operatorname{min}(\{x,y\}), \operatorname{max}(\{x,y\})) \cup A</math>, where <math>A \subseteq \{x,y\}</math>. However, if X is a partially ordered space with order relation '<', then we may describe it thusly: let 'R' denote either '<' or its complement/negative '>'; then, if the endpoints are excluded, "x bi'i y" generates the set <math> \{ \alpha \in X: x </math> R <math> \alpha </math> R <math> y \} </math>. (Notice here that x and y may be presented in either order but for any given selection of presentation order, 'R' is fixed in meaning and present in both relations; if one order of presentation is true, then if the order is switched, then the resulting statement will mean the same thing but the meaning of 'R' will be changed to the other inequality relation. If an endpoint is to be included, this set will just be united with the singleton set of that endpoint. If X cannot be or is not partially ordered, then this present discussion about mathematical representation may be ignored; in such cases, this BIhI construction may still make sense, however - just revert to a more intuitive understanding based on the English description).<br />
*x bi'o y: generates the interval or 'directed' line segment with endpoints x and y in that order (starting from x and going to y); otherwise, it is equivalent to "bi'i". This is the typical meaning of intervals of form [x, y) and the like. Thus "y bi'o x" is backward relative to "x bi'o y". Continuing the discussion in the immediately previous point about "bi'i" which was concerned with nathematical representation of the construct formed, and supposing the same conditions and notation, then "x bi'o y" is exactly the same (and the same commentary applies) except that it demands that 'R' represents '<'. (Notice additionally that, in this case, x < y must be true. However be careful to avoid reading "<" as the symbol representing "less than" in the intuitive sense for real numbers; it could just as easily be any other partial order, including the "greater than" relation).<br />
When X does not "loop around" through the initially-potential intervals in question (it may do so through others): "bi'i" has a symmetry between its two arguments. Thus, it would be weird for conditions to be placed on exactly one of its arguments. "bi'o" is a restriction of "bi'i" which forces a directionality or order upon the line segment produced; thus "bi'o" inherits properties from "bi'i" but the broken symmetry allows conditions to be placed on any combination of its arguments in a natural context.<br />
If X does "loop around" through at least one initially-potential interval at hand, then: "bi'i" forces the 'most natural' or 'minimal' interval to be the one which is being referenced under either ordering of the inputes, and "bi'o" results in the 'most natural' or 'minimal' interval which extends '''from''' the first argument '''to''' the second argument. For example, on a circle, where angles are measured counterclockwise (from the positive x-axis, toward the positive y-axis; an angle of measure <math>0</math> has its rays both being equivalent to the positive x-axis) and where the arguments refer to points on the circle by the angles so measured from the positive x-axis (in radians) at which they are located (modulo <math>\tau = C/r</math> for circle of circumference <math>C</math> and radius <math>r>0</math>): "<math>0</math> bi'o <math>\tau/4</math>" is equivalent to "<math>0</math> bi'i <math>\tau/4</math>" (and, therefore, "<math>\tau/4</math> bi'i <math>0</math>", which is the single arc segment which forms one quarter of the entire circle and which is between the positive x-axis and the positive y-axis; but "<math>\tau/4</math> bi'o <math>0</math>" is entirely different, being the other three quarters of the circle (and, if it matters, this is traced out via having the angle run counterclockwise from positive y-axis (at <math>\tau/4</math>) until it attains the value <math>\tau \equiv 0</math> at the positive x-axis (from 'the other side', so to speak). Throughout this article, X will typically be assumed to not 'loop around' through any initially-potential interval at hand, but the considerations made in this paragraph should apply without too much difficulty in making the analogy.<br />
* (Note that "initially-potential interval" is interpreted broadly, accounting for all conceivable references intended for the interval at hand, which means that X 'loop around' through at least one of the results of "bi'o" and of "se bi'o" for the given arguments (in fixed order); the set of such potential intervals are those which could be meant prior to the audience actually thinking too deeply about the meaning/structure (it is the set of all initial interpretations which are conceivable, regardless of whether they are possible). In this sense, an interval is a path from one of the arguments to the other. Consider a graph/network G of points with some edges. It might be the case that G is a tree (lacks any loops) except for, say, exactly one loop (a sequence of edge-connected nodes such that there is at least one path from at least one node to itself via the edges) which includes a proper subset of its nodes, numbering at least two (for simplicity). As long as both "bi'o" and "se bi'o" do not intersect nonemptily with any of the nodes/edges in this loop, then the loop can be 'excised' from consideration and we can take X to not loop around through any of the initially-potential intervals; in other words X would be the result of 'subtracting' the loop from G; such a subtraction would have no impact on the interval actually meant. On the other hand, if at least one of those intervals does indeed intersect nonemptily with the loop, then X must be taken to 'loop around' through at least one initially-potential interval at hand, and this potential 'looping' must be taken into account when interpreting/evaluating the meaning of the interval being specified).<br />
<br />
It should be noted that, unless <math>x = \pm \infty</math> is defined and true in a given case, <math>\forall r \in [0, + \infty]</math>, "x mi'i r" refers to/forms a bounded interval or the whole space; no semi-infinite (that is: bounded from above/the positive side xor from below/the negative side) interval/line segment (ray) can be produced. The same is true for "bi'i" and "bi'o" if, additionally, r is finite; recall the previous commentary about symmetry of arguments and inheritance concerning these words. These proposals - where '<math>\infty</math>' now refers to any point which has a distance of <math>+ \infty</math> from the origin - will (or, at least, thus far have) not change(d) this fact. In both the current (non-proposed) functionality and the herein proposed functionality, the intervals which are produced by "bi'i" and "bi'o" can be bounded, semi-infinite (in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)), or infinite in both positive and negative directions (doubly-infinite/infinite; in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)).<br />
<br />
If we accept partial orders, the space X can be all sorts of creatures, including - for example - sets under the strict-containment/proper-subset relation (so that BIhI forms an interval of sets). However, more exotic meanings can be used/intended (although any partial order endowing the space would have to be ignored in context with respect to the meaning of BIhI, which is okay and implicitly possible within the description heretofore provided by the CLL). For example, intervals may just trace out (a possibly ordered/'directed') path between points in X, which may be - for example - the geography of locations on Earth, a network, or a set of sets (which may otherwise but inconsequentially for our purposes be endowed with the proper-subset order). In order to be clear: X need not have an order of any kind endowing it overall; however, if "bi'o" is used, the interval generated does have an ordered endowed on it (alone) which may or may not match the order endowing X, should such an order exist.<br />
<br />
A final note for the sake of carefulness: "bi'o" establishes an order on a line segment such that its first argument is somehow 'less' than its second one. However, it does not necessarily/really establish a direction on the line segment in a graph theoretic sense. So, throughout this page, take mentions of directionality with a grain of salt - they may be the result of momentary carelessness.<br />
<br />
=== SE BIhI ===<br />
<br />
Although independent of this whole proposal, SE (specifically "se" and "re'au'e") should be able to precede BIhI. For "bi'i" itself, there would be no effect. For "se bi'o", the order of the arguments is switched so that the first argument of "se bi'o" is the greater/destination endpoint and the second argument thereof is the lesser/origin endpoint. Thus, "bi'i" is equivalent to "bi'o ja se bi'o". For "se mi'i", the order of the arguments is switched so that the first represents the radius length (in one-dimension: half of the length of the linear interval) and the second represents the center of the interval.<br />
<br />
== Proposed Functionality ==<br />
<br />
Any commentary in this article (excluding the 'Authors' and 'Current Functionality' sections) is meant to be taken as part of the "whole proposal". What follows are specific details which are broken into labelled sections for the sake of reference and hierarchy of application.<br />
<br />
=== Main Proposal #1 ===<br />
<br />
Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; fix a basis B thereof. Let r be a nonnegative real number. Let x and y live in the same space X. Define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity. Define B = {<math>e_1, e_2, ..., e_n</math>}. Then there exists <math> x_1, x_2, ..., x_n, y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n), y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let "''R''" denote an 'ordering' relation on F or the ordered field of real numbers (as appropriate) which may be either the "less than" relation (denoted "<") or, as appropriate (determined by GAhO; generically, elliptical), the "less than or equal to" relation (denoted "<math>\leq</math>").<br />
<br />
We let the dimensionality of our space (which is and can be inferred from the dimensionality of x and/or y, which should match) determine the nature of our intervals.<br />
<br />
* "mi'i" is the easiest to redefine. In fact, the previous description needs no reworking, so long as we understand the space to be potentially larger than a line and loosen our notion of "interval". I propose that "x mi'i r" is defined to be/describe the n-dimensional hyperball (or, possibly, the closure thereof) which is centered on/at x and which has radius r. Notationally, it is <math>\{ z \in X: d(x,z)</math> ''R'' <math>r \}</math>.<br />
** In order to be clear: this interval is a neighborhood in the space; that is to say, it is a region of the space which is bounded by and internal to a sphere (but which may possibly include the boundary and/or exclude the center). This region is called a "ball".<br />
** I propose that we adopt additional keywords/glosses/terminology for "mi'i". "mi'i" should be given the keyword/gloss "centered interval"; it might also deserve the keyword/gloss "n-ball". The second argument (here denoted by "r") should be called the "radius" (in addition to "range"). The first argument (here denoted by "x") can remain with the sole label of "center".<br />
* "bi'i" requires a little more work. I propose that "x bi'i y" generates/describes the n-cell/n-orthotope which has opposite vertices at points x and y. This is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (x_i</math> ''R'' <math> \alpha_i </math> ''R'' <math> y_i)) \}</math>.<br />
** This is similar to the rectangle made on a computer by clicking the mouse at one endpoint and holding-with-dragging the cursor to the other endpoint. Note that there are as many ways to generate the same 'rectangle' as there are vertices on/of the 'rectangle' (where this jumber scales with dimensionality of the 'recrangle'). It need not be two-dimensional, though.<br />
** Terminology can again be updated (id est: added to). The interval should be additionally described as a "n-cell" and "n-orthotope interval"; "rectilinear interval" may additionally be considered. Both arguments (here denoted by "x" and "y" respectively) should be labelled as "endpoints". Symmetry between them should be noted in dictionary definitions.<br />
** This extended form of "bi'i" can be obtained via Cartesian products of linear intervals aligned with/generated by the basis elements. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
* "bi'o" has, to me (lai krtisfranks), no obvious extension since (for example) <math>\mathbb{R}^2</math> cannot be ordered.<br />
<br />
_<br />
<br />
When <math>F = \mathbb{R}</math>, 1-tuples/1-dimensional endpoints will be isomorphically mapped automatically to the corresponding real numbers. This allows for ease of use and back-compatibility.<br />
* This is done by establishing the identity/correspondence that <math>\forall (\xi) \in F, (\xi) \leftrightarrow \xi </math>. In other words, the functionality of intervals as defined outside of this whole proposal (which is for the 1-dimensional case) is extended so that endpoints "x" and "y" which are scalars are automatically mapped to (x) and (y) respectively, where the latter are now handled via the extended functionality herein proposed (as a point in (albeit one-dimensional) space and which has coordinates (well, exactly 1 coördinate)).<br />
<br />
Notice that, now, "mi'i" and "bi'i" do not have the same "shape" except when the dimensionality involved is 0 or 1. The former is round whereas the latter is rectilinear. This is assuming Euclidean geometry. If other netrics are involved, they may appear to be the same or may actually be the same. For example, in taxicab geometry, a sphere <i>appears</i> to be a cross-polytope of the appropriate dimensionality, yet it is still a sphere (which bounds "mi'i"-intervals). In Chebyshev geometry, a sphere appears as an orthotope of the appropriate dimensionality, yet it is still a spehere (and the boundary of a "mi'i"-interval); in this case, though, it very well may be congruent to the n-cell (orthotope) that "bi'i" produces (under the proper conditions).<br />
* These distinct definitions are good (utile) and natural in theoretical mathematics.<br />
<br />
=== Alternative #1: Line Segments Unless Specified Otherwise ===<br />
<br />
An alternative (which lai .krtisfranks. finds perhaps even better than the previous proposal (Main Proposal #1)) is to have "bi'i" and "bi'o" always default to referencing line segments (generally: geodesics) in any space. That is, regardless of the space, these two cmavo (but not "mi'i") would 'draw' a line from their first argument to their second one.<br />
<br />
Note: The endpoints (first and second arguments) of "bi'i" and "bi'o" will be points that are specified via multiple coördinates with respect to a basis. They are not merely scalars. They still must live in the same space (X) and thus must have the same number of coördinates. In this situation, the one-dimensional usage which is defined already outside of this whole proposal merely isomorphically maps scalars which are denoted by "x" and "y" to the their corresponding 1-dimensional point specifications "(x)" and "(y)" respectively. (Notice that, without an additional convention, these will never map to "(x,0,0,...)" and "(y,0,0,...)" respectively, despite the isomorphism that may be established. This is meant to avoid the abusive mixing of notation/spaces: there is no interval from (1,2) to 1, for example. We should always specify that the endpoints are higher-dimensional. This note about mapping 1 to (1) is meant solely for the purpose of making this extension back-compatible and natural.)<br />
<br />
This would make the default usage automatically compatible with generalized points (see below). Additionally, line segments are generally useful in geometry of any dimension.<br />
<br />
This also would allow both "bi'i" and "bi'o" to be defined in any decent space (as opposed to only have "bi'i" be defined, which is the case in the aforementioned subproposal).<br />
<br />
In this formulation, "x bi'o y" implies that x is in some sense a starting point of reference/of an imaginary journey and y is the corresponding termination point; both are 'endpoints'/terminals, so to speak. The set produced, however, is still exactly equivalent to that produced by "x bi'i y" and any coloring of the connotations is unmathematical (and, thus, should be avoided in the opinion of lai .krtisfranks.); the latter is generally preferred.<br />
<br />
Note: There is still no established directionality on the linear interval that is produced by "bi'o". However, as long as it does not conflict with any others, we might be able to assume an established order thereupon. "x bi'o y" does mean that "x < y" (along that line).<br />
<br />
In this case, we use "ce'ei'oi" (followed by a number larger than 1 if we are being explicit) on either or both points x, y in the constructs "x bi'i y" and "x bi'o y" in order to produce the swept-out higher-dimensional-orthotopal "interval" that was proposed originally.<br />
<br />
"mi'i" will still generalize to a higher-dimensional-ball in the space. (Its functionality, as described previously, and as extended immediately after this section, is unchanged.)<br />
<br />
=== Proposed Extension A: "mi'i" ===<br />
<br />
"mi'i" can be extended further. Keep the previous definitions and conditions. Now, undefine r. Let <math>r_1, r_2, ..., r_n \geq 0</math>.<br />
<br />
Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just a formal n-tuple which has entries ordered in a corresponding manner - in other words, it isnjust a list of numbers (scalars in thebunderlying field, more specifically) with the order of presentation fixed by the basis of X and according to the utterer's intention. Notice that r does not technically change if the basis is changed; in such a situation, it may not be possible to describe the n-dimensional interval in simple terms (using only linear combinations of the entries of the new basis) at all and, in any case, the utterer would generally need to supply an entirely different list <math> r\prime </math> in order to convey the same thought.<br />
<br />
* Then we can define "x mi'i r" as <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (d_F (x_i, \alpha_i)</math> ''R'' <math>r_i)) \}</math>. Notice that 'd' is now actually '<math>d_F</math>', id est: the metric on the field F. Here, each coordinate of a point <math>\alpha</math> is being compared to the corresponding coordinate of point x; if they are within the specified distance of one another (given by the corresponding entry in the list r), then that coordinate works out; iff all of the coordinates of the point work out, then the point belongs to the interval so described.<br />
** This extended form of "mi'i" can be obtained via Cartesian products of linear intervals. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
<br />
This essentially returns us to the old situation wherein the interval is no longer an n-ball but an n-cell (matching "bi'i"). The side lengths vary (being <math>2 r_i</math> in length, for each side i). The lines which pass through their corresponding/respective midpoints and which are perpendicular to the corresponding hyperfaces will intersect at a single point, videlicet the first argument of "mi'i" constructs (the 'center'; more appropriately: circumcenter), which is the point from which the various perpendicular distances to the boundaries are each measured (being <math> r_i </math>, for the appropriate/corresponding i).<br />
<br />
This definition is good for computer science, graphing, and experimental science. It is almost never used in theoretical mathematics. (Literally never in the experience of lai krtisfranks, at any rate.)<br />
<br />
This additional proposal requires no major update, change, or addition to the glossing/keywords associated with "mi'i" in dictionary definitions, although there would be an implicit understanding of increased generality. If desired, however, "orthotopic interval with given circumcenter" or similar would do nicely.<br />
<br />
* Additionally, we could establish the convention-by-definition that: <math>((\exists \rho \geq 0: ((\forall i \in \mathbb{N} \cap [1, n]), (r_i = \rho))) \implies </math> "x mi'i r" = "x mi'i <math>\rho</math>" <math>)</math>; but we would need a way to ensure that the audience recognizes <math>\rho</math> as an n-tuple and not just a scalar. Otherwise, utilization of this convention would be indistinguishable from the previously-mentioned case/proposal wherein the second argument as a single number constitutes the radius of an n-ball.<br />
** This complication can be overcome by mentioning "ce'ei'oi" immediately after "<math>\rho</math>"; if this is done, then we are to understand that "<math>\rho</math>" represents - in short-hand form - a formal tuple of identical entries (each being <math>\rho</math>). The elements of this tuple must never be negative.<br />
*** If the utterer explicitly defines/declares <math>\rho</math> to be such a formal tuple, then "ce'ei'oi" is not necessary, although it is also not wrong (and may in fact be helpful).<br />
<br />
== Handling Generalized Points ==<br />
<br />
If the input (x and y; the type of one determines the type of the other by forcing it to be the same) are generalized points (such as towns/geographic points), then they likely live in at-least-two-dimensional space, as is the case on Earth. However, with or without Alternative #1, they are being treated as distinct points (assigned real numbers isomorphically if Alternative #1 is not adopted; otherwise, they are free to be points in space). According to this proposal, it is not possible for the interpretation of an interval with these arguments to be anything except one-dimensional. But, for example, maybe we want to discuss the 'rectangular' (more on this immediately later/below) area of the globe between Olympia, Washington, U.S.A. (defined as x) and Tallahassee, Florida, U.S.A. (defined as y). (This rectangle covers much of the continental/contiguous U.S.) "x bi'i y" would, presumably, give the quickest route for a roadtrip or flight from Olympia to Tallahassee (the geodesic line segment (more on this immediately later/below)) or the reverse thereof (from the other to the one); it would not yield the 'rectangle' that we want. The word "ce'ei'oi" fixes this issue. If it is used on a generalized point (rather than a formal tuple - see immediately previous/above ("mi'i" discussion)), then it indicates that that endpoint (and, consequently, all others) is to be treated multi-dimensionally (unless the argument of "ce'ei'oi" is identically and exactly equal to 1). (In order to be clear: in "mi'i", the second argument (the tuple of "radius length(s)") is not considered to be an endpoint for this purpose - or, truly, anywhere within this proposal; it has a distinct nature and possibly typing separate from that of the first argument of "mi'i".) It is not necessary if Alternative #1 is not adopted and if the points are already defined to belong to a well-described space (of known dimensionality) or are decomposed in terms of their basis/represented as a tuple. If we do this, with the former definitions, then "x ce'ei'oi bi'i y" will suddenly indicate not the line(ar interval) between x and y, but instead the 'area between them'. (This area may be visualized thusly: Imagine a map with x and y on it, on a computer. Click on one of these points, drag the cursor to the other. In many programs, a (possibly degenerate) rectangle is swept out, usually with a dashed or dotted outline. The opposite corners of this rectangle are x and y; the remaining corners are given by one coordinate of x and the other coordinate of y, as appropriate. The space highlighted (within this rectangle) is the interval formed.)<br />
<br />
Note that "x ce'ei'oi bi'i y" is equivalent to "x ce'ei'oi bi'i y ce'ei'oi" and to "x bi'i y ce'ei'oi". Likewise if we replace "bi'i" with "bi'o".<br />
<br />
Note that "ce'ei'oi" has to follow the last argument of "bi'i" and "bi'o" when it is used therein and on the right/later side of BIhI and if the right/later BIhI argument is a scalar of nonnegative integer value; else, it will adopt the BIhI argument as its own (instead), unless its own argument is immediately followed by "boi".<br />
<br />
The space in which this interval exists is determined by context. This is a problem even in the unextended (one-dimensional) version of these words in this usage: Is the unordered interval from Paris to London along the Earth's surface (geodesic) or is it a straight line through space (intersecting the Earth's surface at some points as well as the interior)? Is the (un)ordered interval, if geodesic, following the shorter segment of the great-circle connecting the two cities, or the longer one? (The same is true in and with Alternative #1 each.)<br />
<br />
Note that in any case x and y need to live in the same space. So, if one is a generalized point, then the other must be. It makes no sense to discuss the interval from 1 to you or from Olympia to my imaginary friend. Moreover, they must have the same dimensionality; placing "ce'ei'oi" on one of them determines the nature of the other (and so is unnecessary); however, the argument of "ce'ei'oi" does need to be compatible with both x and y if present (for "bi'i" and "bi'o"; this is not the case for its being used upon the first argument of "mi'i", but is indeed the case in its being used on the second argument of "mi'i").<br />
<br />
== Endpoint Clusivity Stati (Inclusion/Exclusion) ==<br />
<br />
=== Notation, Background, Set-Up ===<br />
<br />
Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity; fix a basis B = {<math>e_1, e_2, ..., e_n</math>} thereof. Let x and y live in the same space X. Then there exists <math> x_1, x_2, ..., x_n,\; y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n),\; y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let <math>\rho,\; r_1, r_2, ..., r_n \geq 0</math>. Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just an n-tuple which has entries ordered in a corresponding manner. If n = 1, then we denote: x = (x) = (<math>x_1</math>), y = (y) = (<math>y_1</math>), r = (r) = (<math>r_1</math>).<br />
<br />
Assume at least some of the previous proposals.<br />
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In this section, "endpoint status" (plural: "endpoint stati") and "clusivity" will refer to the options that an utterer has in specifying whether or not the boundary of the (multidimensional) interval is included xor excluded (along certain hyperplanes/manifolds). If such a boundary is included, then we call it "inclusive", "open", "soft", and "rounded" (due to the notation of using rounded brackets ("(" and ")") or an open circle ("○") in graphical/visual depictions). If such a boundary is excluded, then we call it "exclusive", "closed", "hard", and "square"/"sharp" (due to the notation of using square brackets ("[" and "]") or a closed circle ("●") in graphical/visual depictions). Fix an order '<' on the one-dimensional space(s) to at least one of which every linear interval is taken to belong; in each case of occurrence, appropriately redefine "''R''" <math>\in \{ ``<", ``\leq" \}</math> as determined by intent and context.<br />
<br />
A bracket is a symbol which is used in order to denote a piece of the boundary of an interval. It also encodes endpoint status (id est: the clusivity of that part of the boundary). We use rightward-opening brackets for those which, in 1 dimension, bound the space from below/the negative side; these are "(", "[", and "【". "(" denotes such a boundary which is open; "[" denotes such a boundary which is closed; "【" will be used herein as a short-hand way of denoting the general such boundary which may, depending on context, be replaced with "(" and/or "["; this last is called a(n) (opening/rightward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. We use leftward-opening brackets for those which, in 1 dimension, bound the space from above/the positive side; these are ")", "]", and "】". ")" denotes such a boundary which is open; "]" denotes such a boundary which is closed; "】" will be used herein as a short-hand way of denoting the general such boundary which may be, depending on context, be replaced with ")" and/or "]"; this last is called a(n) (closing/leftward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. If it is not clear (especially with the usage of the lenticular brackets, which can assume various values depending on context and which may or may not be interdependent), brackets which pair or depend upon one another will be subscripted with the same label/index as appropriate.<br />
<br />
The status of "【" or of "】" is which of the two options (inclusive or exclusive) it represents in a given instant/context. The status of ''R'' is which of "<" or "<math>\leq</math>" it represents in a given instant/context.<br />
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"<math>\times</math>" denotes the Cartesian product of sets. For sets A and B, <math> A \times B = \{ (a, b):\; a \in A \;\&\; b \in B \}</math>, where (a,b) is a tuple/point with coordinates (namely, in order: a, b) rather than, as the unfortunate notation may suggest, a linear interval from a to b. Note that it is ordered and not commutative. It can be made into a big/serial/iterating operator, denoted: "<math> \times_{i \in C} </math>", where i is an index and it takes every value in a set C subject to the order on C (if there is any).<br />
<br />
Denote: <math>\mathbb{N} \cap [1, n] = \boxdot (n)</math>.<br />
<br />
This section will use "ce'ei'oi" throughout its body. This is done for the sake of eliminating ambiguity and compatibility with all proposals (and alternatives) herein presented.<br />
<br />
Terminology: In "x mi'i r" (for any dimension for x regardless of r) we call x the "center" and r the "radius (length)". Note that, even though it may be called "radius", r really refers to the length in a given dimension. (Radii are really line segments, not the lengths which are associated with them; we abuse terminology here for simplicity.) Any point which has distance from the center (according to the appropriate metric) in a given direction which is exactly equal to the appropriate radius length in the same direction is called an "on-sphere point", "outermost points", or "distant point" of the interval in question. The set of all on-sphere points of an interval is its "outer boundary" or "(outer/minimal enclosing) sphere". Note that "mi'i" may actually generate an n-orthotope (per Proposed Extension A) and thus may not seem or be spherical; the terminology does not vary in order to explicitly and individually account for such cases. The center of a "mi'i" interval is an element of the boundary (which is, generally, partitioned into outer and inner parts; the center is the sole element of the inner part thereof); thus, the center is an endpoint with a clusivity status.<br />
<br />
Terminology: Each (n-1)-side of the n-orthotope produced via interval constructs will be called a "boundary-part" (these are the aforementioned hyperplanes segments); these generalize the notion of "endpoints" (in a slightly different way from how the arguments of BIhI do so) from the one-dimensional case. They may still be called "endpoints" in this article, even though they are not actually points. For a given interval, the set of all such boundary-parts thereof is the boundary of the interval. "mi'i" is taken to have a whole and indivisible outer boundary (without individual boundary-parts) when its dimensionality is greater than 1; when its dimensionality is equal to 1, the two outermost (end)points may be taken to each constitute a boundary-part of the outer boundary; there is an additional (inner) boundary-part, which is exactly the singleton set of the center point.<br />
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''''!'''' '''Important Result''': The n-orthotope formed by "x ce'ei'oi bi'i y (ce'ei'oi)" is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (x_i</math> ''R'' <math>_{-1,i} \alpha_i </math> ''R'' <math>_{1,i} y_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>, where: <math>\forall i \in \boxdot (n)</math>, the status of '【<math>_{i}</math>' is determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{-1,i}</math>' and likewise the status of '】<math>_{i}</math>' is analogously determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{1,i}</math>'.<br />
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=== Current Situation: the One-Dimensional Case ===<br />
<br />
This section is according to (an interpretation of) the CLL.<br />
<br />
In one dimension, we can specify the status of either endpoint of the (linear) interval via use of members of GAhO immediately next to the member of BIhI being used, on the appropriate side. For example, "li no ga'o bi'o ke'i li pa" represents the interval [0, 1). Notice that "ga'o" (which specifies an inclusive endpoint/boundary-part on the negative side) is on the leftern/first-uttered side of "bi'o" (id est: immediately preceding it) and follows "li no"; this means that the lesser endpoint (in this case, the point 0) is to be included. Likewise, "ke'i" (which specifies an exclusive endpoint/boundary-part) is on the rightern/last-uttered side of "bi'o" (id est: immediately following it) and precedes "li pa"; this means that the greater endpoint (in this case, the point 1) is to be excluded.<br />
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The exact same is true if we replace "bi'o" with "bi'i", although we will lose the implication that <math>0 \leq 1</math>.<br />
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Members of GAhO, at least in BIhI constructs, seem to be used - if at all - only adjacent to the member of BIhI itself. lai .krtisfranks. does not know if they are used in any other context or in any other way. There seems, to lai .krtisfranks, to be no recognition nor convention concerning how to interpret the absence of any explicit members of GAhO on one or both sides of BIhI. It does not seem possible, to lai .krtisfranks., for multiple members of GAhO or of BIhI to consecutively succeed one another (of the same selma'o) whilst being 'naked' (id est: with their dictionary meaning, without being quoted or deleted, without being JE- or JOI-connected, etc).<br />
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The structure of a BIhI construct is: [endpoint<sub>1</sub>] (GAhO*) BIhI* (GAhO*) [endpoint<sub>2</sub>].<br />
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=== Assumption/Proposal anent Unmentioned GAhO ===<br />
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The content of this section may count as an additional proposal. In any case, it is assumed throughout the rest of the article.<br />
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If, between an argument of BIhI and the BIhI cmavo itself, there is no explicitly mentioned member of GAhO, then one is still assumed to be present and to apply to and only to the appropriate boundary-part; the clusivity content of an implicit GAhO cmavo, such as in this case, is elliptical/unspecified/vague - it may or may not be determined by context, practicality, or intent, or it may be unimportant (thus, possibly, representative of either possibility).<br />
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For your information: "xau'u'oi" is a member of GAhO which is elliptical with respect to clusivity (status), as described immediately previously. It is proposed separate from and independent of/to this whole proposal or any of its parts. However, the two complement eachother well.<br />
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Whether implicit (as described herein) or explicitly elliptical, such an elliptical clusivity status will be denoted by lenticular brackets in linear intervals.<br />
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It does not make sense for a nontrivial interval of dimensionality at least 1 to neither include nor exclude any given boundary-part in the current framework of what is easily supported and expressible by Lojban; even mathematically and independent of the language, such a statement is true if it is restricted to the one-dimensional case (with end-'''points'''). Therefore, we must assume that one xor the other case applies. Thus, it should not be contentious that this assumption is made.<br />
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=== Proposed Extension B: GAhO with "mi'i", a simple case ===<br />
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There appears to be no prior usage of GAhO with "mi'i" except as proposed [[BPFK Section: Intervals|here]], a notion which lai .krtisfranks. separately formulated in his considerations for this article. The suggestion there is as follows:<br />
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GAhO before "mi'i" indicates the "endpoint status" of the center of the interval. "ga'o" there indicates that the center (the entire internal boundary-part) is definitely included (thereby forming a continuous/contiguous linear interval); the radius-distanced endpoints may or may not be included. "ke'i" there indicates that the center is definitely excluded (thereby forming a broken/punctured linear interval which misses only its center and possibly the radius-distanced endpoints). This usage in nondegenerate cases has no bearing on the clusivity of the radius-distanced endpoints (unless one specifies explicitly that these stati are mutually determinable).<br />
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GAhO after "mi'i" indicates the endpoint status of any point which has distance from the center exactly equal to the radius length specified. "ga'o" here indicates that all of the on-sphere points of the interval are definitely included (causing the outer boundary of the interval to be included; this is pictorially represented by a solid boundary curve). "ke'i" here indicates that all of the on-sphere points of the interval are definitely excluded (causing the outer boundary of the interval to be excluded; this is pictorially represented a dashed/dotted/broken boundary curve). Notice that every on-sphere point shares the same status as every other on-sphere point of a given interval. In nondegenerate cases, this usage has no bearing on the clusivity status of the center of the specified interval (unless one specifies explicitly that these stati are mutually determinable).<br />
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These descriptions apply for the one-dimensional case, but generalize - with little change - to arbritrary dimensionality. The only difference is that the interval generated will be a possibly-punctured line (segment), disc, ball, glome interior, or - generally - n-ball, depending on the dimensionality.<br />
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<br />
Let <math> x \in \mathbb{R}</math>. So, <math> x \leftrightarrow (x)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. These are all one-dimensional:<br />
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* "x mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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<br />
* "x ga'o mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ke'i mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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<br />
* "x mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
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* "x mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
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* "x ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
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* "x ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) < \rho \}</math>.<br />
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* "x ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) \leq \rho \}</math>.<br />
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* "x ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) < \rho \}</math>.<br />
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_<br />
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For emphasis: Even though the forms of the mathematical expressions are approximately the same (similar on first glance) to the analogous expressions for "bi'o", and despite the formal similarities in the Lojban utterances, it is important to realize that <math>\rho</math> here is '''not''' an endpoint of the linear interval. The presence of 'd' in the definition makes a world of difference.<br />
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=== Main Proposal #2 ===<br />
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Recall: dim(X) = n.<br />
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Note: In this section, it is taken to be the case that two mutually adjacent members of GAhO do not compound to form a member of GAhO* (in/as which they cannot be separated).<br />
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It would be nice to be able to specify the status of boundary-parts of higher-dimensional intervals. But there is a great deal of customizability that is available. The pair "vau'e'oi" and (its elidable terminator) "vau'o'oi" handle this.<br />
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The way that they work is as follows:<br />
# "vau'e'oi" opens a scope; this is called the "interval brackets scope" (hereby named "(the) IBS"). The IBS is closed via explicit use of "vau'o'oi", or immediately upon the utterance of any word which is not a member of selma'o GAhO*, or immediately upon the event of the number of explicitly utterred GAhO* members exceeding n. Thus, the only words which may belong within the IBS are members of GAhO* and they number at most n. Any GAhO cmavo explicitly used immediately after the nth explicitly used one in an IBS is ignored.<br />
# The IBS has n ordered slots; these are called "IBS slots" (or, here, just "slots"). Initially, no slots are filled. For each IBS slot, a single explicitly utterred member of GAhO* can fill it. Once one slot is filled, the next explicitly utterred GAhO* member fills the next available slot if possible/it is available. The first explicitly utterred GAhO* member fills the first IBS slot. Members of GAhO* do not need to be separated nor connected from one another in any way. They are Quine-quoted and treated as separate entities '''automatically'''. Thus, no explicit quotes are necessary.<br />
# If the IBS is closed 'prematurely' (id est: before n GAhO* members are explicitly utterred), then any IBS slot which is not explicitly filled at this point is taken to be filled by a vague/elliptical value.<br />
# Syntactically, the IBS result is treated as a single occurrence of GAhO*. Thus the IBS construct must be adjacent to an explicit member of BIhI.<br />
# Semantically/practically, the result is a formal and ordered tuple of interval brackets, the elements of which are the brackets supplied to the IBS in order such that the <math>i</math>th element of the formal tuple produced being the bracket supplied to the <math>i</math>th IBS slot. The location of this result relative to the adjacent BIhI member forces the nature of these brackets (to be rightward-opening iff the result is utterred before/is to the left of the adjacent BIhI member; to be leftward-opening iff the result is utterred after/is to the right of the adjacent BIhI member). Denote this result to be <math>(</math>''B''<math>_1, ...,</math>''B''<math>_n)</math>. Notice that this usage of the character "B" is not the same as elsewhere in this article (where it, for example, may have meant a particar basis); here, it is an individual bracket with a defined clusivity status. The role of this bracket is determined by the location of its IBS with respect to the relevant BIhI; its particular realization with respect to that boundary - that is, its applicability to one or more boundary-parts in that boundary - is determined by the slot which it fills and the basis determined by context.<br />
# The <math>i</math>th member of this tuple (namely, ''B''<math>_i</math>) acts as the corresponding bracket (opening or closing, open or closed) for the <math>i</math>th (component-)interval (parallel to the <math>i</math>th basis element) in the Cartesian product reëxpression/decomposition of the overall interval if such is possible. In other words, the clusivity of the ith hyperplane is that of the bracket B<sub>i</sub>. The order is important and corresponds via index.<br />
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Reiterating: An IBS of n > 0 slots that is closed while having only m slots explicitly filled by GAhO*, where 0 < m < n and m is an integer, has the last n-m slots filled implicitly by an elliptical GAhO* element (with restrictions intuitively/implicitly placed upon it due to context). Notice that GAhO cmavo connected by JE or JOI, for example, form a single element of GAhO* for the purpose of filling slots. There is no separator between filled slots; the GAhO* elements may just be rattled off, separated automatically and filling the slots successively.<br />
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* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> ce'ei'oi (<math>n</math>) vau'e'oi 【<math>_{1}</math> 【<math>_{2}</math> ... 【<math>_{n}</math> (vau'o'oi) bi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(y_1, y_2, ..., y_n)</math> (ce'ei'oi (<math>n</math>))", where <math>(x_1, x_2, ..., x_n)</math> and <math>(y_1, y_2, ..., y_n)</math> are expressed with respect to the basis of the space.<br />
**Notice the lack of commas/separators between brackets. Also note that only one occurrence of "ce'ei'oi" is necessary in this case (since we are working with "bi'i"). The usage of "vau'o'oi" here (in both cases) is optional.<br />
** Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (\alpha_i \in </math>【<math>_i\; x_i,\; y_i </math>】<math>_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>.<br />
*** Thus, we see that the <math>i</math>th opening bracket goes with <math>x_i</math> and the <math>i</math>th closing bracket goes with <math>y_i</math>.<br />
*** Even though it has the same generic form as was expressed in the final part of the previous "Current Functionality" subsection, the meaning is rather different. There, the brackets were elliptical/vague/generic/general. Here, they are specified by the utterrer to be whatsoever was said in the IBS.<br />
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* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> ce'ei'oi (ci) vau'e'oi ga'o ke'i ga'o (vau'o'oi) bi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(y_1, y_2, y_3)</math> (ce'ei'oi (ci)).<br />
** Then <math>I = [x_1 ,\; y_1) \times (x_2 ,\; y_2) \times [x_3 ,\; y_3]</math>. This is the basically the referent of "vei <math>x_1</math> ga'o bi'i ke'i <math>y_1</math> ve'o pi'u vei <math>x_2</math> ke'i bi'i ke'i <math>y_2</math> ve'o pi'u vei <math>x_3</math> ga'o bi'i ga'o <math>y_3</math> ve'o".<br />
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Note that in the precious two examples, so order was imposed on each linear subspace of X. This can be done, mathematically. But it was done here for convenience/for the sake of having established notation in order to make sense of the meaning in a rigorous way. If such order exists on a given linear subspace of X, then all is well for that particular instance of its imposition. However, when interpreting, one must remember to "unimpose"/"unassume" such an ordering. The linear intervals are just specified by two endpoints; the endpoints themselves can be switched (especially systematically). This, however, is a reasonable and semi-canonical way to represent the linear intervals (as long as one remembers that the endpoints need no be in the specified order); it would be confusing to switch only some of them.<br />
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Moral of the story: The IBS causes the brackets that it is given to be sent off to couple with the coordinate to which they belong, in order.<br />
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Postliminarily: It is not grammatical to have naked members of GAhO uttered consecutively in a BIhI construct except when they all are in an IBS (as enclosed by "vau'e'oi" and (possibly elided) "vau'o'oi").<br />
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=== Further Proposal: a Nice and Simple Case for Brackets ===<br />
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The content of this section supposes Main Proposal #2 as being accepted and applicable.<br />
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In this section, back-compatibility, utility/ease, and a simple and nice case are handled.<br />
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What if we do not want to say all of that? How do we support back-compatibility this way? What if all of the brackets submitted is a certain IBS are the same? Well, here is some more functionality: If the last case holds and if "ce'ei'oi" is mentioned so as to apply to an endpoint (rather than a radius length(s) entry), then we can dispense with the IBS altogether. In the multidimensional case, a single bracket ''B'' on a given side of "bi'i" is taken to be isomorphic with the formal ordered interval-bracket tuple (''B'', ..., ''B''), where the number of entries therein is the dimensionality of the space n. Id est: each GAhO cmavo actually constitutes an n-slot IBS such that every entry in it is, explicitly, that very same cmavo. Therefore, "vau'e'oi vau'o'oi" is equivalent to a single instance of "xau'u'oi" alone, allowing for n-dimensionality; this in particular is back-compatible with earlier claims/assumptions/proposals.<br />
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In the case of all the brackets on one side being (of) the same (status), we can just call the tuple by the name of the shared bracket (status). If we are working in an n-dimensional space and we are given only one bracket B outside of an IBS on a given side of "bi'i" explicitly, then we know that the IBS actually should should actually contain n brackets of form B (of the same status). This can work simultaneously on both sides of BIhI.<br />
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In short: "ce'ei'oi n ga'o bi'i" is equivalent to "ce'ei'oi n vau'e'oi ga'o ga'o [...] ga'o vau'o'oi bi'i", where "ga'o" is explicitly mentioned n times in the latter sentence. Analogy/substitution for other cases (such as: using "ke'i", having the brackets on the other side of the BIhI cmavo, or using another cmavo in BIhI) follows by the syntactic uniformity within selma'o.<br />
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Thus, <math>\forall x, y \in \mathbb{R}</math>, "x ga'o bi'i y" is mapped isomorphically to "x (ce'ei'oi pa) vau'e'oi ga'o (vau'o'oi) bi'i (vau'e'oi (vau'o'oi)) y". Recall, of course, that "x" here actually maps to "(x)" isomorphically too, and likewise for "y"; this detail was not shown for clarity, since parentheticals were employed in that example/string in order to represent optional utterrances, and the endpoints are definitely not optional in general.<br />
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Further: At most one naked member of GAhO which is not enclosed by an IBS xor at most one IBS may be explicitly used on a given side of BIhI; any more of either and/or the use of both together is ungrammatical.<br />
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=== Proposed Extension B' ===<br />
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This section assumes adoption of Proposed Extension B. If anything is to be done with "mi'i" (even in the 1-dimensional case) this subproposal (respectively Proposed Extension B) needs to be accepted.<br />
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In "mi'i", the first bracket never needs to be processed through an IBS. Either the center point is included or excluded, and this can be handled one-dimensionally (id est: by just using a member of GAhO on its own). Only one first bracket can be used/appear.<br />
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If "mi'i" is being used in order to produce/describe an n-ball (rather than an n-orthotope, per Proposed Extension A), then only one second (formally "closing") bracket can be used/appear, and- thus- it need not be processed through an IBS. In this case, every on-sphere point is either included xor they are all excluded; specification of this status can be handled one-dimensionally (id est: by just using a member of GAhO on its own).<br />
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Let <math> x \in X</math>. So, <math> x = (x_1, ..., x_n)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. "R" is used, as before, for an inequality relation that may be either strict or loose (the latter admits the possibility for equality). These are all n-dimensional:<br />
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* "x (ce'ei'oi (n)) mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball which may or may not include its external boundary (but whatsoever it does there, it does so to the totality thereof).<br />
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* "x (ce'ei'oi (n)) ga'o mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is an unpunctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ke'i mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a punctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
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* "x (ce'ei'oi (n)) mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely united with its sphere (boundary); it would be drawn with a solid surface on the outside.<br />
* "x (ce'ei'oi (n)) mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely not united with its sphere (boundary); it would be drawn with a broken/dashed/dotted surface on the outside.<br />
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* "x (ce'ei'oi (n)) ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
** This is a closed (solid) unpunctured disc/ball; it definitely includes both its center and its external boundary; it would be drawn with a solid surface on the outside and shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) < \rho \}</math>.<br />
** This is an open unpunctured disc/ball; it definitely includes its center but definitely excludes it external boundary; it would be drawn with a broken/dashed/dotted surface but with shading throughout the interior.<br />
** This is the typical definition of "ball" (or "disc" in two dimensions). It has only interior points, but it has all of them.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) \leq \rho \}</math>.<br />
** This is a punctured disc/ball which is united with its external sphere (external boundary); it definitely includes its external boundary but definitely excludes its center; it would be drawn with a solid surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) < \rho \}</math>.<br />
** This is a punctured disc/ball which excludes its external sphere (external boundary); it definitely excludes both its external boundary and its center; it would be drawn with a broken/dashed/dotted surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
** This is the typical definition of a punctured ball (disc in two dimensions). It is useful for the definition of limit points in topology.<br />
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Clearly, as before, the definitions extend exceptionally easily for this interpretation of "mi'i". In the mathematics, the only formal change in the condition was replacing each "<math>\mathbb{R}</math>" with <math>X</math>. Of course, the points themselves have multiple coordinates and thus the meaning of 'd' gets slightly more complicated, but that is all under the hood (determined by the definition of 'd' and/or intuition about what would be appropriate for the space, given X itself).<br />
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=== Proposed Extension C ===<br />
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This section assumes adoption of Proposed Extension A and Proposed Extension B' (and thus Proposed Extension B).<br />
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If working with "mi'i" where the first argument <math>x = (x_1, ..., x_n)</math> lives in n-dimensional space and if the second argument <math>r = (r_1, ..., r_n)</math> is a formal ordered tuple of n nonnegative extended-real numbers, then an n-cell is produced, in which case "vau'e'oi" and "vau'o'oi" work exactly as before (with "bi'i"). But it is important to note that the IBS can be nontrivial only on the second-argument side of "mi'i".<br />
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Throughout this section, "d" still denotes a distance function on the space X.<br />
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* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 mi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>(x_1, x_2, ..., x_n)</math> is expressed with respect to the basis of the space (and represents a point therein) and <math>r</math> formally corresponds via indices coordinatewise.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.<br />
** If, here, '【' = '(' here, let <math>C = \{ (x_1 , x_2 , x_3) \} </math>, id est the singleton of the central point; if, here, '【' = '[', then let <math> C = \{ \} </math>. Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in [0,\; r_i </math>】<math>_i)) \} \setminus C</math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ga'o (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3]</math>.<br />
*** Notice that, despite the inclusion status of the first argument, the leftern brackets in the Cartesian expression of this orthotope have varied clusivity status. The important thing is that the intervals are continuous (not missing their central point x<sub>i</sub>) due to the explicit presence of "ga'o" immediately before "mi'i"; the clusivity stati of the leftern bracket and of the rightern bracket in each Cartesian-productand should mutually match - and they are determined determined by the member of GAhO in the corresponding ISB slot in the ISB immediately following "mi'i".<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ke'i (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = \big( (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3] \big) \setminus (x_1 , x_2 , x_3 ) </math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = ((x_1 - r_1 ,\; x_1) \cup (x_1 ,\;x_1 + r_1)) \times ((x_2 - r_2 ,\; x_2) \cup (x_2 ,\;x_2 + r_2)) \times ([x_3 - r_3 ,\; x_3) \cup (x_3 ,\;x_3 + r_3])</math>.<br />
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== Vocabulary/Semantics that have been Introduced ==<br />
<br />
Mostly, old vocabulary has been expanded in functionality.<br />
<br />
'''Old/CLL vocabulary with expanded functionality''':<br />
*mi'i - Originally, this word denotes/construct a line or line segment which was (taken to be) centered on the point specified by the first argument and which had length specified by the second argument. Main Proposal #1 allows "mi'i" to denote/construct a volume in n dimensions which is bounded by a sphere which is centered at the point specified by the first argument and which is of the radius specified by the second argument. Proposed Extension A allows "mi'i" to denote/construct a volume enclosed by an n-orthotope with axes parallel to those of the space (the basis) such that each side has a distance from the point, specified by the first argument, which is equal to the corresponding entry in the list which is specified by the second argument; if all entries in the list which is the second argument are the same, then the second argument may be represented by just that number via the use of "ce'ei'oi" (see later).<br />
*bi'i - Originally, this word denotes/constructs a line, linear ray, or line segment in one-dimensional space between two specified points (rays have one such point being infinite; lines have both being infinite). Main Proposal #1 extends the functionality so that this word denotes/constructs a volume enclosed by an n-orthotope in n-dimensional space (which may have any, all, or none of its faces/sides at infinity), such that each axis thereof is parallel to one axis of the space (defined by a single element of the basis); the two arguments of "bi'i" specify some pair of mutually opposite vertices on the n-orthotope - there coordinates with respect to the relevant basis determine the corresponding sides and are the corresponding endpoints in an expression of the generated volume by Cartesian product of one-dimensional linear intervals (which may be given by CLL/old "bi'i" itself).<br />
*bi'o - Originally, this word acted as "bi'i" does with the further assumption that the first argument is lesser/the origin and the second argument is greater/the destination. Its functionality was not really generalized in this whole proposal.<br />
*ga'o/ke'i - If every bracket in an IBS (see "vau'e'oi", later) would be explicitly specified as a single particular member of GAhO, then the whole IBS may be abbreviated to/represented by a single instance of the same unenclosed in an IBS.<br />
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For all of these, if the points specified are one-dimensional, generic/geographic, or cannot be specified in terms of a tuple of coordinates (as given by the basis of the space), then they may be represented by a simple point/name (not enclosed in a tuple), which is isomorphic to a one-tuple of only that entry.<br />
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<br />
'''New vocabulary''':<br />
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*ce'ei'oi<br />
*vau'e'oi<br />
*vau'o'oi<br />
*IBS<br />
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'''Independent vocabulary''':<br />
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*xau'u'oi<br />
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== Miscellany ==<br />
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"mi'i" is really good for error bars in the sciences. In English, scientists often say stuff like "g is 9.85 plus-or-minus .05 meters per second per second". This is abusive. The only options for the value of g in such a case would be 9.80 m/s<sup>2</sup> or 9.90 m/s<sup>2</sup>. What they mean is that the value of g is between these two values (possibly including either of them). Following the format of the example quote, we have "mi'i" being the intention, with 9.85 functioning as the center and .05 as the radius. In describing a data set, one should make sure to say that the variable (usually dependent) ''belongs'' to this set, rather than it ''being'' this set. This variable will be the one with error bars in the graph. If a single variable is described in such a manner, the error bars graphically are parallel to only one axis: the actual value (as measured, within standard deviation/error) can shift in this direction (so long as it remains within the bars) but cannot shift in any other. If the error bars are applied to the ''point'', rather than the ''variable'' (which acts as a coordinate of the former), though, then the error bar will (under this proposal) envelop the point in a ball of the given radius; the actual value (as measured, within standard deviation/error) could thus shift in any direction within n-space so long as it remains within the provided radius of the given (measured, central) value. Adopting Proposed Extension A, each coordinate can be individually and independently assigned/associated with an error; the error bars will graphically be parallel to each axis (or will be 0); the actual value (as measured, within standard deviation/error for each measurement/variable/coordinate) can shift relative to the data point along each axis so long as it stays within the axis-appropriate radius of the data point.<br />
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=== Further Ideas ===<br />
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* It may be beneficial to us to figure out a system by which to generate basic shapes such a convex hulls via specification of important points (or sets of points). The current framework does not support such generalization since only two arguments of BIhI are presently allowed.<br />
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* We may want a separate word for or modifier of "mi'i", here denoted by "<u>'''NTRVL'''</u>", such that: for <math>I \prime</math> being the interval generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 <u>'''NTRVL'''</u> vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>x = (x_1, x_2, ..., x_n) \in X</math> is expressed with respect to the basis of the space <math>X</math> (and represents a point therein) and <math>r = (r_1, r_2, ..., r_n)</math> formally corresponds via indices coordinatewise, then <math>I \prime = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Extended_Dimensionality_of_Interval_cmavo&diff=123217Extended Dimensionality of Interval cmavo2019-05-23T15:01:56Z<p>Krtisfranks: /* Current Functionality */ - added information</p>
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<div>{{jbocre/en}}<br />
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Presently, the cmavo "mi'i", "bi'i", "bi'o" (which currently constitute all elements of selma'o BIhI) all represent/create one-dimensional intervals. However, in mathematics and even in daily life, there are many instances when higher-dimensional intervals are desired. This functionality should be supported.<br />
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Rather than creating new cmavo for this task, the current cmavo (aforementioned) can simply be extended. The proposal described here will have the objective of supporting functionality for description of higher-dimensional intervals via extension only; only mathematical points are being discussed. The result should be back-compatible.<br />
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== Contributors ==<br />
<br />
The following people have contributed to the writing of this article (or have provided ideas for it):<br />
*lai .krtisfranks.<br />
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Where first-person personal pronouns are used, they refer to at least one of these individuals. However, they will be avoided whensoever possible (with explicit mention of the author's name when a personal opinion or insight is conveyed).<br />
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== Current Functionality ==<br />
<br />
The cmavo of BIhI are nonlogical interval connectives. In mathematics (other options are available), one inputs a real number or possibly a generic endpoint, follows it by a cmavo of BIhI, and then mentions another real number or endpoint. The result is a description of a set of all points belonging to an interval. More explicitly:<br />
<br />
Let x and y be real numbers or points in geometric space, let r be a nonnegative real number. Let the space to which x and y belong be X. Further suppose that X does not "loop around" in any sense. Then:<br />
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*x mi'i r: generates the interval centered on x which has range r on either side of x; in other words, this is the set of all points that have a distance to x that is less than (or possibly equal to) r. x is the midpoint of the interval, which has length 2r. Such a thing is sometimes denoted in a fashion similar to <math> \operatorname{B}_1 (x, r) </math>, where "B" is for "ball" and the subscript "1" tells the dimensionality of the space; this is also called an r neighborhood of x (sometimes denoted <math> \operatorname{nbhd} (x, r) </math>), where the space is inferred from context.<br />
*x bi'i y: generates the interval or unordered line segment with endpoints x and y; in other words, this is the set of all points between x and y (possibly including either, both, or neither of the endpoints). "y bi'i x" is completely equivalent to "x bi'i y"; there is no inherent order to the inputs nor direction to the line segment. This is the generic meaning for "between" when referring to an interval, in normal life or in mathematics; there is no notation for this notion which is both commonly understood and known to lai .krtisfranks. ; supposing an ordering on X, the closest thing would be an interval of form: <math>(\operatorname{min}(\{x,y\}), \operatorname{max}(\{x,y\})) \cup A</math>, where <math>A \subseteq \{x,y\}</math>. However, if X is a partially ordered space with order relation '<', then we may describe it thusly: let 'R' denote either '<' or its complement/negative '>'; then, if the endpoints are excluded, "x bi'i y" generates the set <math> \{ \alpha \in X: x </math> R <math> \alpha </math> R <math> y \} </math>. (Notice here that x and y may be presented in either order but for any given selection of presentation order, 'R' is fixed in meaning and present in both relations; if one order of presentation is true, then if the order is switched, then the resulting statement will mean the same thing but the meaning of 'R' will be changed to the other inequality relation. If an endpoint is to be included, this set will just be united with the singleton set of that endpoint. If X cannot be or is not partially ordered, then this present discussion about mathematical representation may be ignored; in such cases, this BIhI construction may still make sense, however - just revert to a more intuitive understanding based on the English description).<br />
*x bi'o y: generates the interval or 'directed' line segment with endpoints x and y in that order (starting from x and going to y); otherwise, it is equivalent to "bi'i". This is the typical meaning of intervals of form [x, y) and the like. Thus "y bi'o x" is backward relative to "x bi'o y". Continuing the discussion in the immediately previous point about "bi'i" which was concerned with nathematical representation of the construct formed, and supposing the same conditions and notation, then "x bi'o y" is exactly the same (and the same commentary applies) except that it demands that 'R' represents '<'. (Notice additionally that, in this case, x < y must be true. However be careful to avoid reading "<" as the symbol representing "less than" in the intuitive sense for real numbers; it could just as easily be any other partial order, including the "greater than" relation).<br />
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When X does not "loop around" through the initially-potential intervals in question (it may do so through others): "bi'i" has a symmetry between its two arguments. Thus, it would be weird for conditions to be placed on exactly one of its arguments. "bi'o" is a restriction of "bi'i" which forces a directionality or order upon the line segment produced; thus "bi'o" inherits properties from "bi'i" but the broken symmetry allows conditions to be placed on any combination of its arguments in a natural context.<br />
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If X does "loop around" through at least one initially-potential interval at hand, then: "bi'i" forces the 'most natural' or 'minimal' interval to be the one which is being referenced under either ordering of the inputes, and "bi'o" results in the 'most natural' or 'minimal' interval which extends '''from''' the first argument '''to''' the second argument. For example, on a circle, where angles are measured counterclockwise (from the positive x-axis, toward the positive y-axis; an angle of measure <math>0</math> has its rays both being equivalent to the positive x-axis) and where the arguments refer to points on the circle by the angles so measured from the positive x-axis (in radians) at which they are located (modulo <math>\tau = C/r</math> for circle of circumference <math>C</math> and radius <math>r>0</math>): "<math>0</math> bi'o <math>\tau/4</math>" is equivalent to "<math>0</math> bi'i <math>\tau/4</math>" (and, therefore, "<math>\tau/4</math> bi'i <math>0</math>", which is the single arc segment which forms one quarter of the entire circle and which is between the positive x-axis and the positive y-axis; but "<math>\tau/4</math> bi'o <math>0</math>" is entirely different, being the other three quarters of the circle (and, if it matters, this is traced out via having the angle run counterclockwise from positive y-axis (at <math>\tau/4</math>) until it attains the value <math>\tau \equiv 0</math> at the positive x-axis (from 'the other side', so to speak). Throughout this article, X will typically be assumed to not 'loop around' through any initially-potential interval at hand, but the considerations made in this paragraph should apply without too much difficulty in making the analogy.<br />
* (Note that "initially-potential interval" is interpreted broadly, accounting for all conceivable references intended for the interval at hand, which means that X 'loop around' through at least one of the results of "bi'o" and of "se bi'o" for the given arguments (in fixed order); the set of such potential intervals are those which could be meant prior to the audience actually thinking too deeply about the meaning/structure (it is the set of all initial interpretations which are conceivable, regardless of whether they are possible). In this sense, an interval is a path from one of the arguments to the other. Consider a graph/network G of points with some edges. It might be the case that G is a tree (lacks any loops) except for, say, exactly one loop (a sequence of edge-connected nodes such that there is at least one path from at least one node to itself via the edges) which includes a proper subset of its nodes, numbering at least two (for simplicity). As long as both "bi'o" and "se bi'o" do not intersect nonemptily with any of the nodes/edges in this loop, then the loop can be 'excised' from consideration and we can take X to not loop around through any of the initially-potential intervals; in other words X would be the result of 'subtracting' the loop from G; such a subtraction would have no impact on the interval actually meant. On the other hand, if at least one of those intervals does indeed intersect nonemptily with the loop, then X must be taken to 'loop around' through at least one initially-potential interval at hand, and this potential 'looping' must be taken into account when interpreting/evaluating the meaning of the interval being specified).<br />
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It should be noted that, unless <math>x = \pm \infty</math> is defined and true in a given case, <math>\forall r \in [0, + \infty]</math>, "x mi'i r" refers to/forms a bounded interval or the whole space; no semi-infinite (that is: bounded from above/the positive side xor from below/the negative side) interval/line segment (ray) can be produced. The same is true for "bi'i" and "bi'o" if, additionally, r is finite; recall the previous commentary about symmetry of arguments and inheritance concerning these words. These proposals - where '<math>\infty</math>' now refers to any point which has a distance of <math>+ \infty</math> from the origin - will (or, at least, thus far have) not change(d) this fact. In both the current (non-proposed) functionality and the herein proposed functionality, the intervals which are produced by "bi'i" and "bi'o" can be bounded, semi-infinite (in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)), or infinite in both positive and negative directions (doubly-infinite/infinite; in any number of directions (so long as that number is a nonnegative integer less than or equal to the dimensionality of the space)).<br />
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If we accept partial orders, the space X can be all sorts of creatures, including - for example - sets under the strict-containment/proper-subset relation (so that BIhI forms an interval of sets). However, more exotic meanings can be used/intended (although any partial order endowing the space would have to be ignored in context with respect to the meaning of BIhI, which is okay and implicitly possible within the description heretofore provided by the CLL). For example, intervals may just trace out (a possibly ordered/'directed') path between points in X, which may be - for example - the geography of locations on Earth, a network, or a set of sets (which may otherwise but inconsequentially for our purposes be endowed with the proper-subset order). In order to be clear: X need not have an order of any kind endowing it overall; however, if "bi'o" is used, the interval generated does have an ordered endowed on it (alone) which may or may not match the order endowing X, should such an order exist.<br />
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A final note for the sake of carefulness: "bi'o" establishes an order on a line segment such that its first argument is somehow 'less' than its second one. However, it does not necessarily/really establish a direction on the line segment in a graph theoretic sense. So, throughout this page, take mentions of directionality with a grain of salt - they may be the result of momentary carelessness.<br />
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=== SE BIhI ===<br />
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Although independent of this whole proposal, SE (specifically "se" and "re'au'e") should be able to precede BIhI. For "bi'i" itself, there would be no effect. For "se bi'o", the order of the arguments is switched so that the first argument of "se bi'o" is the greater/destination endpoint and the second argument thereof is the lesser/origin endpoint. Thus, "bi'i" is equivalent to "bi'o ja se bi'o". For "se mi'i", the order of the arguments is switched so that the first represents the radius length (in one-dimension: half of the length of the linear interval) and the second represents the center of the interval.<br />
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== Proposed Functionality ==<br />
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Any commentary in this article (excluding the 'Authors' and 'Current Functionality' sections) is meant to be taken as part of the "whole proposal". What follows are specific details which are broken into labelled sections for the sake of reference and hierarchy of application.<br />
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=== Main Proposal #1 ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; fix a basis B thereof. Let r be a nonnegative real number. Let x and y live in the same space X. Define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity. Define B = {<math>e_1, e_2, ..., e_n</math>}. Then there exists <math> x_1, x_2, ..., x_n, y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n), y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let "''R''" denote an 'ordering' relation on F or the ordered field of real numbers (as appropriate) which may be either the "less than" relation (denoted "<") or, as appropriate (determined by GAhO; generically, elliptical), the "less than or equal to" relation (denoted "<math>\leq</math>").<br />
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We let the dimensionality of our space (which is and can be inferred from the dimensionality of x and/or y, which should match) determine the nature of our intervals.<br />
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* "mi'i" is the easiest to redefine. In fact, the previous description needs no reworking, so long as we understand the space to be potentially larger than a line and loosen our notion of "interval". I propose that "x mi'i r" is defined to be/describe the n-dimensional hyperball (or, possibly, the closure thereof) which is centered on/at x and which has radius r. Notationally, it is <math>\{ z \in X: d(x,z)</math> ''R'' <math>r \}</math>.<br />
** In order to be clear: this interval is a neighborhood in the space; that is to say, it is a region of the space which is bounded by and internal to a sphere (but which may possibly include the boundary and/or exclude the center). This region is called a "ball".<br />
** I propose that we adopt additional keywords/glosses/terminology for "mi'i". "mi'i" should be given the keyword/gloss "centered interval"; it might also deserve the keyword/gloss "n-ball". The second argument (here denoted by "r") should be called the "radius" (in addition to "range"). The first argument (here denoted by "x") can remain with the sole label of "center".<br />
* "bi'i" requires a little more work. I propose that "x bi'i y" generates/describes the n-cell/n-orthotope which has opposite vertices at points x and y. This is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (x_i</math> ''R'' <math> \alpha_i </math> ''R'' <math> y_i)) \}</math>.<br />
** This is similar to the rectangle made on a computer by clicking the mouse at one endpoint and holding-with-dragging the cursor to the other endpoint. Note that there are as many ways to generate the same 'rectangle' as there are vertices on/of the 'rectangle' (where this jumber scales with dimensionality of the 'recrangle'). It need not be two-dimensional, though.<br />
** Terminology can again be updated (id est: added to). The interval should be additionally described as a "n-cell" and "n-orthotope interval"; "rectilinear interval" may additionally be considered. Both arguments (here denoted by "x" and "y" respectively) should be labelled as "endpoints". Symmetry between them should be noted in dictionary definitions.<br />
** This extended form of "bi'i" can be obtained via Cartesian products of linear intervals aligned with/generated by the basis elements. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
* "bi'o" has, to me (lai krtisfranks), no obvious extension since (for example) <math>\mathbb{R}^2</math> cannot be ordered.<br />
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_<br />
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When <math>F = \mathbb{R}</math>, 1-tuples/1-dimensional endpoints will be isomorphically mapped automatically to the corresponding real numbers. This allows for ease of use and back-compatibility.<br />
* This is done by establishing the identity/correspondence that <math>\forall (\xi) \in F, (\xi) \leftrightarrow \xi </math>. In other words, the functionality of intervals as defined outside of this whole proposal (which is for the 1-dimensional case) is extended so that endpoints "x" and "y" which are scalars are automatically mapped to (x) and (y) respectively, where the latter are now handled via the extended functionality herein proposed (as a point in (albeit one-dimensional) space and which has coordinates (well, exactly 1 coördinate)).<br />
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Notice that, now, "mi'i" and "bi'i" do not have the same "shape" except when the dimensionality involved is 0 or 1. The former is round whereas the latter is rectilinear. This is assuming Euclidean geometry. If other netrics are involved, they may appear to be the same or may actually be the same. For example, in taxicab geometry, a sphere <i>appears</i> to be a cross-polytope of the appropriate dimensionality, yet it is still a sphere (which bounds "mi'i"-intervals). In Chebyshev geometry, a sphere appears as an orthotope of the appropriate dimensionality, yet it is still a spehere (and the boundary of a "mi'i"-interval); in this case, though, it very well may be congruent to the n-cell (orthotope) that "bi'i" produces (under the proper conditions).<br />
* These distinct definitions are good (utile) and natural in theoretical mathematics.<br />
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=== Alternative #1: Line Segments Unless Specified Otherwise ===<br />
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An alternative (which lai .krtisfranks. finds perhaps even better than the previous proposal (Main Proposal #1)) is to have "bi'i" and "bi'o" always default to referencing line segments (generally: geodesics) in any space. That is, regardless of the space, these two cmavo (but not "mi'i") would 'draw' a line from their first argument to their second one.<br />
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Note: The endpoints (first and second arguments) of "bi'i" and "bi'o" will be points that are specified via multiple coördinates with respect to a basis. They are not merely scalars. They still must live in the same space (X) and thus must have the same number of coördinates. In this situation, the one-dimensional usage which is defined already outside of this whole proposal merely isomorphically maps scalars which are denoted by "x" and "y" to the their corresponding 1-dimensional point specifications "(x)" and "(y)" respectively. (Notice that, without an additional convention, these will never map to "(x,0,0,...)" and "(y,0,0,...)" respectively, despite the isomorphism that may be established. This is meant to avoid the abusive mixing of notation/spaces: there is no interval from (1,2) to 1, for example. We should always specify that the endpoints are higher-dimensional. This note about mapping 1 to (1) is meant solely for the purpose of making this extension back-compatible and natural.)<br />
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This would make the default usage automatically compatible with generalized points (see below). Additionally, line segments are generally useful in geometry of any dimension.<br />
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This also would allow both "bi'i" and "bi'o" to be defined in any decent space (as opposed to only have "bi'i" be defined, which is the case in the aforementioned subproposal).<br />
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In this formulation, "x bi'o y" implies that x is in some sense a starting point of reference/of an imaginary journey and y is the corresponding termination point; both are 'endpoints'/terminals, so to speak. The set produced, however, is still exactly equivalent to that produced by "x bi'i y" and any coloring of the connotations is unmathematical (and, thus, should be avoided in the opinion of lai .krtisfranks.); the latter is generally preferred.<br />
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Note: There is still no established directionality on the linear interval that is produced by "bi'o". However, as long as it does not conflict with any others, we might be able to assume an established order thereupon. "x bi'o y" does mean that "x < y" (along that line).<br />
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In this case, we use "ce'ei'oi" (followed by a number larger than 1 if we are being explicit) on either or both points x, y in the constructs "x bi'i y" and "x bi'o y" in order to produce the swept-out higher-dimensional-orthotopal "interval" that was proposed originally.<br />
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"mi'i" will still generalize to a higher-dimensional-ball in the space. (Its functionality, as described previously, and as extended immediately after this section, is unchanged.)<br />
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=== Proposed Extension A: "mi'i" ===<br />
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"mi'i" can be extended further. Keep the previous definitions and conditions. Now, undefine r. Let <math>r_1, r_2, ..., r_n \geq 0</math>.<br />
<br />
Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just a formal n-tuple which has entries ordered in a corresponding manner - in other words, it isnjust a list of numbers (scalars in thebunderlying field, more specifically) with the order of presentation fixed by the basis of X and according to the utterer's intention. Notice that r does not technically change if the basis is changed; in such a situation, it may not be possible to describe the n-dimensional interval in simple terms (using only linear combinations of the entries of the new basis) at all and, in any case, the utterer would generally need to supply an entirely different list <math> r\prime </math> in order to convey the same thought.<br />
<br />
* Then we can define "x mi'i r" as <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X: ((\forall i \in \mathbb{N} \cap [1, n]), (d_F (x_i, \alpha_i)</math> ''R'' <math>r_i)) \}</math>. Notice that 'd' is now actually '<math>d_F</math>', id est: the metric on the field F. Here, each coordinate of a point <math>\alpha</math> is being compared to the corresponding coordinate of point x; if they are within the specified distance of one another (given by the corresponding entry in the list r), then that coordinate works out; iff all of the coordinates of the point work out, then the point belongs to the interval so described.<br />
** This extended form of "mi'i" can be obtained via Cartesian products of linear intervals. We will exploit this fact in the discussion about the endpoint stati (see the section named accordingly).<br />
<br />
This essentially returns us to the old situation wherein the interval is no longer an n-ball but an n-cell (matching "bi'i"). The side lengths vary (being <math>2 r_i</math> in length, for each side i). The lines which pass through their corresponding/respective midpoints and which are perpendicular to the corresponding hyperfaces will intersect at a single point, videlicet the first argument of "mi'i" constructs (the 'center'; more appropriately: circumcenter), which is the point from which the various perpendicular distances to the boundaries are each measured (being <math> r_i </math>, for the appropriate/corresponding i).<br />
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This definition is good for computer science, graphing, and experimental science. It is almost never used in theoretical mathematics. (Literally never in the experience of lai krtisfranks, at any rate.)<br />
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This additional proposal requires no major update, change, or addition to the glossing/keywords associated with "mi'i" in dictionary definitions, although there would be an implicit understanding of increased generality. If desired, however, "orthotopic interval with given circumcenter" or similar would do nicely.<br />
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* Additionally, we could establish the convention-by-definition that: <math>((\exists \rho \geq 0: ((\forall i \in \mathbb{N} \cap [1, n]), (r_i = \rho))) \implies </math> "x mi'i r" = "x mi'i <math>\rho</math>" <math>)</math>; but we would need a way to ensure that the audience recognizes <math>\rho</math> as an n-tuple and not just a scalar. Otherwise, utilization of this convention would be indistinguishable from the previously-mentioned case/proposal wherein the second argument as a single number constitutes the radius of an n-ball.<br />
** This complication can be overcome by mentioning "ce'ei'oi" immediately after "<math>\rho</math>"; if this is done, then we are to understand that "<math>\rho</math>" represents - in short-hand form - a formal tuple of identical entries (each being <math>\rho</math>). The elements of this tuple must never be negative.<br />
*** If the utterer explicitly defines/declares <math>\rho</math> to be such a formal tuple, then "ce'ei'oi" is not necessary, although it is also not wrong (and may in fact be helpful).<br />
<br />
== Handling Generalized Points ==<br />
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If the input (x and y; the type of one determines the type of the other by forcing it to be the same) are generalized points (such as towns/geographic points), then they likely live in at-least-two-dimensional space, as is the case on Earth. However, with or without Alternative #1, they are being treated as distinct points (assigned real numbers isomorphically if Alternative #1 is not adopted; otherwise, they are free to be points in space). According to this proposal, it is not possible for the interpretation of an interval with these arguments to be anything except one-dimensional. But, for example, maybe we want to discuss the 'rectangular' (more on this immediately later/below) area of the globe between Olympia, Washington, U.S.A. (defined as x) and Tallahassee, Florida, U.S.A. (defined as y). (This rectangle covers much of the continental/contiguous U.S.) "x bi'i y" would, presumably, give the quickest route for a roadtrip or flight from Olympia to Tallahassee (the geodesic line segment (more on this immediately later/below)) or the reverse thereof (from the other to the one); it would not yield the 'rectangle' that we want. The word "ce'ei'oi" fixes this issue. If it is used on a generalized point (rather than a formal tuple - see immediately previous/above ("mi'i" discussion)), then it indicates that that endpoint (and, consequently, all others) is to be treated multi-dimensionally (unless the argument of "ce'ei'oi" is identically and exactly equal to 1). (In order to be clear: in "mi'i", the second argument (the tuple of "radius length(s)") is not considered to be an endpoint for this purpose - or, truly, anywhere within this proposal; it has a distinct nature and possibly typing separate from that of the first argument of "mi'i".) It is not necessary if Alternative #1 is not adopted and if the points are already defined to belong to a well-described space (of known dimensionality) or are decomposed in terms of their basis/represented as a tuple. If we do this, with the former definitions, then "x ce'ei'oi bi'i y" will suddenly indicate not the line(ar interval) between x and y, but instead the 'area between them'. (This area may be visualized thusly: Imagine a map with x and y on it, on a computer. Click on one of these points, drag the cursor to the other. In many programs, a (possibly degenerate) rectangle is swept out, usually with a dashed or dotted outline. The opposite corners of this rectangle are x and y; the remaining corners are given by one coordinate of x and the other coordinate of y, as appropriate. The space highlighted (within this rectangle) is the interval formed.)<br />
<br />
Note that "x ce'ei'oi bi'i y" is equivalent to "x ce'ei'oi bi'i y ce'ei'oi" and to "x bi'i y ce'ei'oi". Likewise if we replace "bi'i" with "bi'o".<br />
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Note that "ce'ei'oi" has to follow the last argument of "bi'i" and "bi'o" when it is used therein and on the right/later side of BIhI and if the right/later BIhI argument is a scalar of nonnegative integer value; else, it will adopt the BIhI argument as its own (instead), unless its own argument is immediately followed by "boi".<br />
<br />
The space in which this interval exists is determined by context. This is a problem even in the unextended (one-dimensional) version of these words in this usage: Is the unordered interval from Paris to London along the Earth's surface (geodesic) or is it a straight line through space (intersecting the Earth's surface at some points as well as the interior)? Is the (un)ordered interval, if geodesic, following the shorter segment of the great-circle connecting the two cities, or the longer one? (The same is true in and with Alternative #1 each.)<br />
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Note that in any case x and y need to live in the same space. So, if one is a generalized point, then the other must be. It makes no sense to discuss the interval from 1 to you or from Olympia to my imaginary friend. Moreover, they must have the same dimensionality; placing "ce'ei'oi" on one of them determines the nature of the other (and so is unnecessary); however, the argument of "ce'ei'oi" does need to be compatible with both x and y if present (for "bi'i" and "bi'o"; this is not the case for its being used upon the first argument of "mi'i", but is indeed the case in its being used on the second argument of "mi'i").<br />
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== Endpoint Clusivity Stati (Inclusion/Exclusion) ==<br />
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=== Notation, Background, Set-Up ===<br />
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Fix a space X which is endowed with a metric d and defined over an ordered field F which is also endowed with a compatible metric <math>d_F</math>; define the dimensionality of X to be dim(X) = n, where n is any nonnegative integer or (for simplicity: countable) infinity; fix a basis B = {<math>e_1, e_2, ..., e_n</math>} thereof. Let x and y live in the same space X. Then there exists <math> x_1, x_2, ..., x_n,\; y_1, y_2, ..., y_n \in F: x = x_1 e_1 +...+ x_n e_n = (x_1, ..., x_n),\; y = y_1 e_1 +...+ y_n e_n = (y_1, ..., y_n)</math>. Let <math>\rho,\; r_1, r_2, ..., r_n \geq 0</math>. Then we can express a new formal tuple <math>r = (r_1, ..., r_n)</math> where the order of the entries correspond to similarly labelled coordinates of points in X with respect to the basis established. Note that r does not live in X; it is just an n-tuple which has entries ordered in a corresponding manner. If n = 1, then we denote: x = (x) = (<math>x_1</math>), y = (y) = (<math>y_1</math>), r = (r) = (<math>r_1</math>).<br />
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Assume at least some of the previous proposals.<br />
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In this section, "endpoint status" (plural: "endpoint stati") and "clusivity" will refer to the options that an utterer has in specifying whether or not the boundary of the (multidimensional) interval is included xor excluded (along certain hyperplanes/manifolds). If such a boundary is included, then we call it "inclusive", "open", "soft", and "rounded" (due to the notation of using rounded brackets ("(" and ")") or an open circle ("○") in graphical/visual depictions). If such a boundary is excluded, then we call it "exclusive", "closed", "hard", and "square"/"sharp" (due to the notation of using square brackets ("[" and "]") or a closed circle ("●") in graphical/visual depictions). Fix an order '<' on the one-dimensional space(s) to at least one of which every linear interval is taken to belong; in each case of occurrence, appropriately redefine "''R''" <math>\in \{ ``<", ``\leq" \}</math> as determined by intent and context.<br />
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A bracket is a symbol which is used in order to denote a piece of the boundary of an interval. It also encodes endpoint status (id est: the clusivity of that part of the boundary). We use rightward-opening brackets for those which, in 1 dimension, bound the space from below/the negative side; these are "(", "[", and "【". "(" denotes such a boundary which is open; "[" denotes such a boundary which is closed; "【" will be used herein as a short-hand way of denoting the general such boundary which may, depending on context, be replaced with "(" and/or "["; this last is called a(n) (opening/rightward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. We use leftward-opening brackets for those which, in 1 dimension, bound the space from above/the positive side; these are ")", "]", and "】". ")" denotes such a boundary which is open; "]" denotes such a boundary which is closed; "】" will be used herein as a short-hand way of denoting the general such boundary which may be, depending on context, be replaced with ")" and/or "]"; this last is called a(n) (closing/leftward-opening) lenticular bracket; its conveyed endpoint status is semantically elliptical in nature. If it is not clear (especially with the usage of the lenticular brackets, which can assume various values depending on context and which may or may not be interdependent), brackets which pair or depend upon one another will be subscripted with the same label/index as appropriate.<br />
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The status of "【" or of "】" is which of the two options (inclusive or exclusive) it represents in a given instant/context. The status of ''R'' is which of "<" or "<math>\leq</math>" it represents in a given instant/context.<br />
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"<math>\times</math>" denotes the Cartesian product of sets. For sets A and B, <math> A \times B = \{ (a, b):\; a \in A \;\&\; b \in B \}</math>, where (a,b) is a tuple/point with coordinates (namely, in order: a, b) rather than, as the unfortunate notation may suggest, a linear interval from a to b. Note that it is ordered and not commutative. It can be made into a big/serial/iterating operator, denoted: "<math> \times_{i \in C} </math>", where i is an index and it takes every value in a set C subject to the order on C (if there is any).<br />
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Denote: <math>\mathbb{N} \cap [1, n] = \boxdot (n)</math>.<br />
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This section will use "ce'ei'oi" throughout its body. This is done for the sake of eliminating ambiguity and compatibility with all proposals (and alternatives) herein presented.<br />
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Terminology: In "x mi'i r" (for any dimension for x regardless of r) we call x the "center" and r the "radius (length)". Note that, even though it may be called "radius", r really refers to the length in a given dimension. (Radii are really line segments, not the lengths which are associated with them; we abuse terminology here for simplicity.) Any point which has distance from the center (according to the appropriate metric) in a given direction which is exactly equal to the appropriate radius length in the same direction is called an "on-sphere point", "outermost points", or "distant point" of the interval in question. The set of all on-sphere points of an interval is its "outer boundary" or "(outer/minimal enclosing) sphere". Note that "mi'i" may actually generate an n-orthotope (per Proposed Extension A) and thus may not seem or be spherical; the terminology does not vary in order to explicitly and individually account for such cases. The center of a "mi'i" interval is an element of the boundary (which is, generally, partitioned into outer and inner parts; the center is the sole element of the inner part thereof); thus, the center is an endpoint with a clusivity status.<br />
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Terminology: Each (n-1)-side of the n-orthotope produced via interval constructs will be called a "boundary-part" (these are the aforementioned hyperplanes segments); these generalize the notion of "endpoints" (in a slightly different way from how the arguments of BIhI do so) from the one-dimensional case. They may still be called "endpoints" in this article, even though they are not actually points. For a given interval, the set of all such boundary-parts thereof is the boundary of the interval. "mi'i" is taken to have a whole and indivisible outer boundary (without individual boundary-parts) when its dimensionality is greater than 1; when its dimensionality is equal to 1, the two outermost (end)points may be taken to each constitute a boundary-part of the outer boundary; there is an additional (inner) boundary-part, which is exactly the singleton set of the center point.<br />
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''''!'''' '''Important Result''': The n-orthotope formed by "x ce'ei'oi bi'i y (ce'ei'oi)" is <math>\{ \alpha = \alpha_1 e_1 +...+ \alpha_n e_n = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (x_i</math> ''R'' <math>_{-1,i} \alpha_i </math> ''R'' <math>_{1,i} y_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>, where: <math>\forall i \in \boxdot (n)</math>, the status of '【<math>_{i}</math>' is determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{-1,i}</math>' and likewise the status of '】<math>_{i}</math>' is analogously determined by/isomorphic/logical equivalence with/to the status of ' ''R''<math>_{1,i}</math>'.<br />
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=== Current Situation: the One-Dimensional Case ===<br />
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This section is according to (an interpretation of) the CLL.<br />
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In one dimension, we can specify the status of either endpoint of the (linear) interval via use of members of GAhO immediately next to the member of BIhI being used, on the appropriate side. For example, "li no ga'o bi'o ke'i li pa" represents the interval [0, 1). Notice that "ga'o" (which specifies an inclusive endpoint/boundary-part on the negative side) is on the leftern/first-uttered side of "bi'o" (id est: immediately preceding it) and follows "li no"; this means that the lesser endpoint (in this case, the point 0) is to be included. Likewise, "ke'i" (which specifies an exclusive endpoint/boundary-part) is on the rightern/last-uttered side of "bi'o" (id est: immediately following it) and precedes "li pa"; this means that the greater endpoint (in this case, the point 1) is to be excluded.<br />
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The exact same is true if we replace "bi'o" with "bi'i", although we will lose the implication that <math>0 \leq 1</math>.<br />
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Members of GAhO, at least in BIhI constructs, seem to be used - if at all - only adjacent to the member of BIhI itself. lai .krtisfranks. does not know if they are used in any other context or in any other way. There seems, to lai .krtisfranks, to be no recognition nor convention concerning how to interpret the absence of any explicit members of GAhO on one or both sides of BIhI. It does not seem possible, to lai .krtisfranks., for multiple members of GAhO or of BIhI to consecutively succeed one another (of the same selma'o) whilst being 'naked' (id est: with their dictionary meaning, without being quoted or deleted, without being JE- or JOI-connected, etc).<br />
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The structure of a BIhI construct is: [endpoint<sub>1</sub>] (GAhO*) BIhI* (GAhO*) [endpoint<sub>2</sub>].<br />
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=== Assumption/Proposal anent Unmentioned GAhO ===<br />
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The content of this section may count as an additional proposal. In any case, it is assumed throughout the rest of the article.<br />
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If, between an argument of BIhI and the BIhI cmavo itself, there is no explicitly mentioned member of GAhO, then one is still assumed to be present and to apply to and only to the appropriate boundary-part; the clusivity content of an implicit GAhO cmavo, such as in this case, is elliptical/unspecified/vague - it may or may not be determined by context, practicality, or intent, or it may be unimportant (thus, possibly, representative of either possibility).<br />
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For your information: "xau'u'oi" is a member of GAhO which is elliptical with respect to clusivity (status), as described immediately previously. It is proposed separate from and independent of/to this whole proposal or any of its parts. However, the two complement eachother well.<br />
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Whether implicit (as described herein) or explicitly elliptical, such an elliptical clusivity status will be denoted by lenticular brackets in linear intervals.<br />
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It does not make sense for a nontrivial interval of dimensionality at least 1 to neither include nor exclude any given boundary-part in the current framework of what is easily supported and expressible by Lojban; even mathematically and independent of the language, such a statement is true if it is restricted to the one-dimensional case (with end-'''points'''). Therefore, we must assume that one xor the other case applies. Thus, it should not be contentious that this assumption is made.<br />
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=== Proposed Extension B: GAhO with "mi'i", a simple case ===<br />
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There appears to be no prior usage of GAhO with "mi'i" except as proposed [[BPFK Section: Intervals|here]], a notion which lai .krtisfranks. separately formulated in his considerations for this article. The suggestion there is as follows:<br />
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GAhO before "mi'i" indicates the "endpoint status" of the center of the interval. "ga'o" there indicates that the center (the entire internal boundary-part) is definitely included (thereby forming a continuous/contiguous linear interval); the radius-distanced endpoints may or may not be included. "ke'i" there indicates that the center is definitely excluded (thereby forming a broken/punctured linear interval which misses only its center and possibly the radius-distanced endpoints). This usage in nondegenerate cases has no bearing on the clusivity of the radius-distanced endpoints (unless one specifies explicitly that these stati are mutually determinable).<br />
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GAhO after "mi'i" indicates the endpoint status of any point which has distance from the center exactly equal to the radius length specified. "ga'o" here indicates that all of the on-sphere points of the interval are definitely included (causing the outer boundary of the interval to be included; this is pictorially represented by a solid boundary curve). "ke'i" here indicates that all of the on-sphere points of the interval are definitely excluded (causing the outer boundary of the interval to be excluded; this is pictorially represented a dashed/dotted/broken boundary curve). Notice that every on-sphere point shares the same status as every other on-sphere point of a given interval. In nondegenerate cases, this usage has no bearing on the clusivity status of the center of the specified interval (unless one specifies explicitly that these stati are mutually determinable).<br />
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These descriptions apply for the one-dimensional case, but generalize - with little change - to arbritrary dimensionality. The only difference is that the interval generated will be a possibly-punctured line (segment), disc, ball, glome interior, or - generally - n-ball, depending on the dimensionality.<br />
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Let <math> x \in \mathbb{R}</math>. So, <math> x \leftrightarrow (x)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. These are all one-dimensional:<br />
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* "x mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ga'o mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x ke'i mi'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
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* "x mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
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* "x mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
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* "x ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
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* "x ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 \leq d(x,z) < \rho \}</math>.<br />
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* "x ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) \leq \rho \}</math>.<br />
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* "x ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z \in \mathbb{R} :\; 0 < d(x,z) < \rho \}</math>.<br />
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_<br />
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For emphasis: Even though the forms of the mathematical expressions are approximately the same (similar on first glance) to the analogous expressions for "bi'o", and despite the formal similarities in the Lojban utterances, it is important to realize that <math>\rho</math> here is '''not''' an endpoint of the linear interval. The presence of 'd' in the definition makes a world of difference.<br />
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=== Main Proposal #2 ===<br />
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Recall: dim(X) = n.<br />
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Note: In this section, it is taken to be the case that two mutually adjacent members of GAhO do not compound to form a member of GAhO* (in/as which they cannot be separated).<br />
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It would be nice to be able to specify the status of boundary-parts of higher-dimensional intervals. But there is a great deal of customizability that is available. The pair "vau'e'oi" and (its elidable terminator) "vau'o'oi" handle this.<br />
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The way that they work is as follows:<br />
# "vau'e'oi" opens a scope; this is called the "interval brackets scope" (hereby named "(the) IBS"). The IBS is closed via explicit use of "vau'o'oi", or immediately upon the utterance of any word which is not a member of selma'o GAhO*, or immediately upon the event of the number of explicitly utterred GAhO* members exceeding n. Thus, the only words which may belong within the IBS are members of GAhO* and they number at most n. Any GAhO cmavo explicitly used immediately after the nth explicitly used one in an IBS is ignored.<br />
# The IBS has n ordered slots; these are called "IBS slots" (or, here, just "slots"). Initially, no slots are filled. For each IBS slot, a single explicitly utterred member of GAhO* can fill it. Once one slot is filled, the next explicitly utterred GAhO* member fills the next available slot if possible/it is available. The first explicitly utterred GAhO* member fills the first IBS slot. Members of GAhO* do not need to be separated nor connected from one another in any way. They are Quine-quoted and treated as separate entities '''automatically'''. Thus, no explicit quotes are necessary.<br />
# If the IBS is closed 'prematurely' (id est: before n GAhO* members are explicitly utterred), then any IBS slot which is not explicitly filled at this point is taken to be filled by a vague/elliptical value.<br />
# Syntactically, the IBS result is treated as a single occurrence of GAhO*. Thus the IBS construct must be adjacent to an explicit member of BIhI.<br />
# Semantically/practically, the result is a formal and ordered tuple of interval brackets, the elements of which are the brackets supplied to the IBS in order such that the <math>i</math>th element of the formal tuple produced being the bracket supplied to the <math>i</math>th IBS slot. The location of this result relative to the adjacent BIhI member forces the nature of these brackets (to be rightward-opening iff the result is utterred before/is to the left of the adjacent BIhI member; to be leftward-opening iff the result is utterred after/is to the right of the adjacent BIhI member). Denote this result to be <math>(</math>''B''<math>_1, ...,</math>''B''<math>_n)</math>. Notice that this usage of the character "B" is not the same as elsewhere in this article (where it, for example, may have meant a particar basis); here, it is an individual bracket with a defined clusivity status. The role of this bracket is determined by the location of its IBS with respect to the relevant BIhI; its particular realization with respect to that boundary - that is, its applicability to one or more boundary-parts in that boundary - is determined by the slot which it fills and the basis determined by context.<br />
# The <math>i</math>th member of this tuple (namely, ''B''<math>_i</math>) acts as the corresponding bracket (opening or closing, open or closed) for the <math>i</math>th (component-)interval (parallel to the <math>i</math>th basis element) in the Cartesian product reëxpression/decomposition of the overall interval if such is possible. In other words, the clusivity of the ith hyperplane is that of the bracket B<sub>i</sub>. The order is important and corresponds via index.<br />
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Reiterating: An IBS of n > 0 slots that is closed while having only m slots explicitly filled by GAhO*, where 0 < m < n and m is an integer, has the last n-m slots filled implicitly by an elliptical GAhO* element (with restrictions intuitively/implicitly placed upon it due to context). Notice that GAhO cmavo connected by JE or JOI, for example, form a single element of GAhO* for the purpose of filling slots. There is no separator between filled slots; the GAhO* elements may just be rattled off, separated automatically and filling the slots successively.<br />
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* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> ce'ei'oi (<math>n</math>) vau'e'oi 【<math>_{1}</math> 【<math>_{2}</math> ... 【<math>_{n}</math> (vau'o'oi) bi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(y_1, y_2, ..., y_n)</math> (ce'ei'oi (<math>n</math>))", where <math>(x_1, x_2, ..., x_n)</math> and <math>(y_1, y_2, ..., y_n)</math> are expressed with respect to the basis of the space.<br />
**Notice the lack of commas/separators between brackets. Also note that only one occurrence of "ce'ei'oi" is necessary in this case (since we are working with "bi'i"). The usage of "vau'o'oi" here (in both cases) is optional.<br />
** Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; (\alpha_i \in </math>【<math>_i\; x_i,\; y_i </math>】<math>_i)) \} = \times_{i \in \boxdot (n)} \;(</math>【<math>_{i}\; x_i,\; y_i </math>】<math>_{i} \;)</math>.<br />
*** Thus, we see that the <math>i</math>th opening bracket goes with <math>x_i</math> and the <math>i</math>th closing bracket goes with <math>y_i</math>.<br />
*** Even though it has the same generic form as was expressed in the final part of the previous "Current Functionality" subsection, the meaning is rather different. There, the brackets were elliptical/vague/generic/general. Here, they are specified by the utterrer to be whatsoever was said in the IBS.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> ce'ei'oi (ci) vau'e'oi ga'o ke'i ga'o (vau'o'oi) bi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(y_1, y_2, y_3)</math> (ce'ei'oi (ci)).<br />
** Then <math>I = [x_1 ,\; y_1) \times (x_2 ,\; y_2) \times [x_3 ,\; y_3]</math>. This is the basically the referent of "vei <math>x_1</math> ga'o bi'i ke'i <math>y_1</math> ve'o pi'u vei <math>x_2</math> ke'i bi'i ke'i <math>y_2</math> ve'o pi'u vei <math>x_3</math> ga'o bi'i ga'o <math>y_3</math> ve'o".<br />
<br />
Note that in the precious two examples, so order was imposed on each linear subspace of X. This can be done, mathematically. But it was done here for convenience/for the sake of having established notation in order to make sense of the meaning in a rigorous way. If such order exists on a given linear subspace of X, then all is well for that particular instance of its imposition. However, when interpreting, one must remember to "unimpose"/"unassume" such an ordering. The linear intervals are just specified by two endpoints; the endpoints themselves can be switched (especially systematically). This, however, is a reasonable and semi-canonical way to represent the linear intervals (as long as one remembers that the endpoints need no be in the specified order); it would be confusing to switch only some of them.<br />
<br />
Moral of the story: The IBS causes the brackets that it is given to be sent off to couple with the coordinate to which they belong, in order.<br />
<br />
Postliminarily: It is not grammatical to have naked members of GAhO uttered consecutively in a BIhI construct except when they all are in an IBS (as enclosed by "vau'e'oi" and (possibly elided) "vau'o'oi").<br />
<br />
=== Further Proposal: a Nice and Simple Case for Brackets ===<br />
<br />
The content of this section supposes Main Proposal #2 as being accepted and applicable.<br />
<br />
In this section, back-compatibility, utility/ease, and a simple and nice case are handled.<br />
<br />
What if we do not want to say all of that? How do we support back-compatibility this way? What if all of the brackets submitted is a certain IBS are the same? Well, here is some more functionality: If the last case holds and if "ce'ei'oi" is mentioned so as to apply to an endpoint (rather than a radius length(s) entry), then we can dispense with the IBS altogether. In the multidimensional case, a single bracket ''B'' on a given side of "bi'i" is taken to be isomorphic with the formal ordered interval-bracket tuple (''B'', ..., ''B''), where the number of entries therein is the dimensionality of the space n. Id est: each GAhO cmavo actually constitutes an n-slot IBS such that every entry in it is, explicitly, that very same cmavo. Therefore, "vau'e'oi vau'o'oi" is equivalent to a single instance of "xau'u'oi" alone, allowing for n-dimensionality; this in particular is back-compatible with earlier claims/assumptions/proposals.<br />
<br />
In the case of all the brackets on one side being (of) the same (status), we can just call the tuple by the name of the shared bracket (status). If we are working in an n-dimensional space and we are given only one bracket B outside of an IBS on a given side of "bi'i" explicitly, then we know that the IBS actually should should actually contain n brackets of form B (of the same status). This can work simultaneously on both sides of BIhI.<br />
<br />
In short: "ce'ei'oi n ga'o bi'i" is equivalent to "ce'ei'oi n vau'e'oi ga'o ga'o [...] ga'o vau'o'oi bi'i", where "ga'o" is explicitly mentioned n times in the latter sentence. Analogy/substitution for other cases (such as: using "ke'i", having the brackets on the other side of the BIhI cmavo, or using another cmavo in BIhI) follows by the syntactic uniformity within selma'o.<br />
<br />
Thus, <math>\forall x, y \in \mathbb{R}</math>, "x ga'o bi'i y" is mapped isomorphically to "x (ce'ei'oi pa) vau'e'oi ga'o (vau'o'oi) bi'i (vau'e'oi (vau'o'oi)) y". Recall, of course, that "x" here actually maps to "(x)" isomorphically too, and likewise for "y"; this detail was not shown for clarity, since parentheticals were employed in that example/string in order to represent optional utterrances, and the endpoints are definitely not optional in general.<br />
<br />
Further: At most one naked member of GAhO which is not enclosed by an IBS xor at most one IBS may be explicitly used on a given side of BIhI; any more of either and/or the use of both together is ungrammatical.<br />
<br />
=== Proposed Extension B' ===<br />
<br />
This section assumes adoption of Proposed Extension B. If anything is to be done with "mi'i" (even in the 1-dimensional case) this subproposal (respectively Proposed Extension B) needs to be accepted.<br />
<br />
In "mi'i", the first bracket never needs to be processed through an IBS. Either the center point is included or excluded, and this can be handled one-dimensionally (id est: by just using a member of GAhO on its own). Only one first bracket can be used/appear.<br />
<br />
If "mi'i" is being used in order to produce/describe an n-ball (rather than an n-orthotope, per Proposed Extension A), then only one second (formally "closing") bracket can be used/appear, and- thus- it need not be processed through an IBS. In this case, every on-sphere point is either included xor they are all excluded; specification of this status can be handled one-dimensionally (id est: by just using a member of GAhO on its own).<br />
<br />
<br />
<br />
Let <math> x \in X</math>. So, <math> x = (x_1, ..., x_n)</math>. Recall: <math>\rho \geq 0</math>. Also, 'd' denotes the distance in this space; note that it is positive-definite. "R" is used, as before, for an inequality relation that may be either strict or loose (the latter admits the possibility for equality). These are all n-dimensional:<br />
<br />
* "x (ce'ei'oi (n)) mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball which may or may not include its external boundary (but whatsoever it does there, it does so to the totality thereof).<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; \leq\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is an unpunctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ke'i mi'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; <\; d(x,z)\; </math> ''R''<math>\; \rho \}</math>.<br />
** This is a punctured disc/ball; it may or may not be united with its sphere (boundary); it would be drawn with shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
<br />
<br />
* "x (ce'ei'oi (n)) mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; \leq\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely united with its sphere (boundary); it would be drawn with a solid surface on the outside.<br />
* "x (ce'ei'oi (n)) mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0\; </math> ''R'' <math>\; d(x,z)\; <\; \rho \}</math>.<br />
** This is a possibly punctured disc/ball that is definitely not united with its sphere (boundary); it would be drawn with a broken/dashed/dotted surface on the outside.<br />
<br />
<br />
* "x (ce'ei'oi (n)) ga'o mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) \leq \rho \}</math>.<br />
** This is a closed (solid) unpunctured disc/ball; it definitely includes both its center and its external boundary; it would be drawn with a solid surface on the outside and shading throughout the interior.<br />
* "x (ce'ei'oi (n)) ga'o mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 \leq d(x,z) < \rho \}</math>.<br />
** This is an open unpunctured disc/ball; it definitely includes its center but definitely excludes it external boundary; it would be drawn with a broken/dashed/dotted surface but with shading throughout the interior.<br />
** This is the typical definition of "ball" (or "disc" in two dimensions). It has only interior points, but it has all of them.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ga'o <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) \leq \rho \}</math>.<br />
** This is a punctured disc/ball which is united with its external sphere (external boundary); it definitely includes its external boundary but definitely excludes its center; it would be drawn with a solid surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
* "x (ce'ei'oi (n)) ke'i mi'i ke'i <math>\rho</math>" means: <math>\{ z = (z_1, ..., z_n) \in X :\; 0 < d(x,z) < \rho \}</math>.<br />
** This is a punctured disc/ball which excludes its external sphere (external boundary); it definitely excludes both its external boundary and its center; it would be drawn with a broken/dashed/dotted surface and shading throughout the interior except at the center, where a small open and unshaded ball would be drawn/notated.<br />
** This is the typical definition of a punctured ball (disc in two dimensions). It is useful for the definition of limit points in topology.<br />
<br />
<br />
Clearly, as before, the definitions extend exceptionally easily for this interpretation of "mi'i". In the mathematics, the only formal change in the condition was replacing each "<math>\mathbb{R}</math>" with <math>X</math>. Of course, the points themselves have multiple coordinates and thus the meaning of 'd' gets slightly more complicated, but that is all under the hood (determined by the definition of 'd' and/or intuition about what would be appropriate for the space, given X itself).<br />
<br />
=== Proposed Extension C ===<br />
<br />
This section assumes adoption of Proposed Extension A and Proposed Extension B' (and thus Proposed Extension B).<br />
<br />
If working with "mi'i" where the first argument <math>x = (x_1, ..., x_n)</math> lives in n-dimensional space and if the second argument <math>r = (r_1, ..., r_n)</math> is a formal ordered tuple of n nonnegative extended-real numbers, then an n-cell is produced, in which case "vau'e'oi" and "vau'o'oi" work exactly as before (with "bi'i"). But it is important to note that the IBS can be nontrivial only on the second-argument side of "mi'i".<br />
<br />
Throughout this section, "d" still denotes a distance function on the space X.<br />
<br />
<br />
<br />
* Example: Consider the interval <math>I</math> generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 mi'i vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>(x_1, x_2, ..., x_n)</math> is expressed with respect to the basis of the space (and represents a point therein) and <math>r</math> formally corresponds via indices coordinatewise.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.<br />
** If, here, '【' = '(' here, let <math>C = \{ (x_1 , x_2 , x_3) \} </math>, id est the singleton of the central point; if, here, '【' = '[', then let <math> C = \{ \} </math>. Then <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in [0,\; r_i </math>】<math>_i)) \} \setminus C</math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ga'o (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3]</math>.<br />
*** Notice that, despite the inclusion status of the first argument, the leftern brackets in the Cartesian expression of this orthotope have varied clusivity status. The important thing is that the intervals are continuous (not missing their central point x<sub>i</sub>) due to the explicit presence of "ga'o" immediately before "mi'i"; the clusivity stati of the leftern bracket and of the rightern bracket in each Cartesian-productand should mutually match - and they are determined determined by the member of GAhO in the corresponding ISB slot in the ISB immediately following "mi'i".<br />
* Example: Consider <math>I</math> generated/named by "<math>(x_1, x_2, x_3)</math> (ce'ei'oi (ci)) (vau'e'oi) ke'i (vau'o'oi) mi'i vau'e'oi ke'i ke'i ga'o (vau'o'oi) <math>(r_1, r_2, r_3)</math> ce'ei'oi (ci).<br />
** Then <math>I = \big( (x_1 - r_1 ,\; x_1 + r_1) \times (x_2 - r_2 ,\; x_2 + r_2) \times [x_3 - r_3 ,\; x_3 + r_3] \big) \setminus (x_1 , x_2 , x_3 ) </math>.<br />
*** Notice that it is <u>'''NOT'''</u>: <math>I = ((x_1 - r_1 ,\; x_1) \cup (x_1 ,\;x_1 + r_1)) \times ((x_2 - r_2 ,\; x_2) \cup (x_2 ,\;x_2 + r_2)) \times ([x_3 - r_3 ,\; x_3) \cup (x_3 ,\;x_3 + r_3])</math>.<br />
<br />
== Vocabulary/Semantics that have been Introduced ==<br />
<br />
Mostly, old vocabulary has been expanded in functionality.<br />
<br />
'''Old/CLL vocabulary with expanded functionality''':<br />
*mi'i - Originally, this word denotes/construct a line or line segment which was (taken to be) centered on the point specified by the first argument and which had length specified by the second argument. Main Proposal #1 allows "mi'i" to denote/construct a volume in n dimensions which is bounded by a sphere which is centered at the point specified by the first argument and which is of the radius specified by the second argument. Proposed Extension A allows "mi'i" to denote/construct a volume enclosed by an n-orthotope with axes parallel to those of the space (the basis) such that each side has a distance from the point, specified by the first argument, which is equal to the corresponding entry in the list which is specified by the second argument; if all entries in the list which is the second argument are the same, then the second argument may be represented by just that number via the use of "ce'ei'oi" (see later).<br />
*bi'i - Originally, this word denotes/constructs a line, linear ray, or line segment in one-dimensional space between two specified points (rays have one such point being infinite; lines have both being infinite). Main Proposal #1 extends the functionality so that this word denotes/constructs a volume enclosed by an n-orthotope in n-dimensional space (which may have any, all, or none of its faces/sides at infinity), such that each axis thereof is parallel to one axis of the space (defined by a single element of the basis); the two arguments of "bi'i" specify some pair of mutually opposite vertices on the n-orthotope - there coordinates with respect to the relevant basis determine the corresponding sides and are the corresponding endpoints in an expression of the generated volume by Cartesian product of one-dimensional linear intervals (which may be given by CLL/old "bi'i" itself).<br />
*bi'o - Originally, this word acted as "bi'i" does with the further assumption that the first argument is lesser/the origin and the second argument is greater/the destination. Its functionality was not really generalized in this whole proposal.<br />
*ga'o/ke'i - If every bracket in an IBS (see "vau'e'oi", later) would be explicitly specified as a single particular member of GAhO, then the whole IBS may be abbreviated to/represented by a single instance of the same unenclosed in an IBS.<br />
<br />
For all of these, if the points specified are one-dimensional, generic/geographic, or cannot be specified in terms of a tuple of coordinates (as given by the basis of the space), then they may be represented by a simple point/name (not enclosed in a tuple), which is isomorphic to a one-tuple of only that entry.<br />
<br />
<br />
'''New vocabulary''':<br />
<br />
*ce'ei'oi<br />
*vau'e'oi<br />
*vau'o'oi<br />
*IBS<br />
<br />
'''Independent vocabulary''':<br />
<br />
*xau'u'oi<br />
<br />
== Miscellany ==<br />
<br />
"mi'i" is really good for error bars in the sciences. In English, scientists often say stuff like "g is 9.85 plus-or-minus .05 meters per second per second". This is abusive. The only options for the value of g in such a case would be 9.80 m/s<sup>2</sup> or 9.90 m/s<sup>2</sup>. What they mean is that the value of g is between these two values (possibly including either of them). Following the format of the example quote, we have "mi'i" being the intention, with 9.85 functioning as the center and .05 as the radius. In describing a data set, one should make sure to say that the variable (usually dependent) ''belongs'' to this set, rather than it ''being'' this set. This variable will be the one with error bars in the graph. If a single variable is described in such a manner, the error bars graphically are parallel to only one axis: the actual value (as measured, within standard deviation/error) can shift in this direction (so long as it remains within the bars) but cannot shift in any other. If the error bars are applied to the ''point'', rather than the ''variable'' (which acts as a coordinate of the former), though, then the error bar will (under this proposal) envelop the point in a ball of the given radius; the actual value (as measured, within standard deviation/error) could thus shift in any direction within n-space so long as it remains within the provided radius of the given (measured, central) value. Adopting Proposed Extension A, each coordinate can be individually and independently assigned/associated with an error; the error bars will graphically be parallel to each axis (or will be 0); the actual value (as measured, within standard deviation/error for each measurement/variable/coordinate) can shift relative to the data point along each axis so long as it stays within the axis-appropriate radius of the data point.<br />
<br />
=== Further Ideas ===<br />
<br />
* It may be beneficial to us to figure out a system by which to generate basic shapes such a convex hulls via specification of important points (or sets of points). The current framework does not support such generalization since only two arguments of BIhI are presently allowed.<br />
<br />
* We may want a separate word for or modifier of "mi'i", here denoted by "<u>'''NTRVL'''</u>", such that: for <math>I \prime</math> being the interval generated/named by "<math>(x_1, x_2, ..., x_n)</math> (ce'ei'oi (<math>n</math>)) 【 <u>'''NTRVL'''</u> vau'e'oi 】<math>_{1}</math> 】<math>_{2}</math> ... 】<math>_{n}\;\;</math> (vau'o'oi) <math>(r_1, r_2, ..., r_n)</math> ce'ei'oi (<math>n</math>)", where <math>x = (x_1, x_2, ..., x_n) \in X</math> is expressed with respect to the basis of the space <math>X</math> (and represents a point therein) and <math>r = (r_1, r_2, ..., r_n)</math> formally corresponds via indices coordinatewise, then <math>I \prime = \{ \alpha = (\alpha_1, ..., \alpha_n) \in X:\; ((\forall i \in \boxdot (n)),\; ( d(x_i, \alpha_i) \in </math>【 <math>0,\; r_i </math>】<math>_i)) \}</math>.<br />
** Notice that the second instance of "ce'ei'oi" is necessary since we '''must''' specify that we have a formal ordered tuple of radii lengths. In neither case is explicit mention of n necessary as an argument of "ce'ei'oi", provided that the audience knows the size of the tuple r and/or the dimensionality of the space X (which is to say the number of coordinates of x; all of these must match).<br />
*** Of course, if the tuple r is specified explicitly, especially entry-by-entry, or if everyone knows that it is a formal ordered nontrivial tuple, then "ce'ei'oi" is not necessary. Additionally, if r is trivial (in the sense of having at most one entry), then "ce'ei'oi" is elidable by convention.<br />
** Notice that the first-uttered/leftern bracket is alone.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123184experimental rafsi2019-01-10T18:44:45Z<p>Krtisfranks: /* Proposed and Unofficial */ - "pe'a"</p>
<hr />
<div>== Introduction and Classification ==<br />
<br />
Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
Additionally, this page tends to focus on individual, atomic, and self-contained proposals which do not have larger effects, proposals, projects, or ideas behind them - with notable exceptions for series (such as for hexadecimal digits, drag-and-drop selbri-conversion, FA, etc.); in time, hopefully, additional discussions which touch on or which would be strongly affected by experimental rafsi can be added or linked to (such as in a "See Also" section).<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
**: Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
***: No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
***: ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-tez-'''" for "{{jvs|te'o}}" also. See: "{{jvs|tezda}}".<br />
** "'''-cix-'''" for "{{jvs|ci'i}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
** "'''-xox-'''" for "{{jvs|xo}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gav-'''" for "{{jvs|grava}}".<br />
* "'''-vul-'''" for "{{jvs|vubla}}".<br />
* "'''-xig-'''" for "{{jvs|xigzo}}".<br />
* "'''-mug-'''" for "{{jvs|mugle}}".<br />
* "'''-xob-'''" for "{{jvs|xonba}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
* "{{jvs|kamre}}" probably could use a cmarafsi too, but I ([[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]])) am not sure what to do for it at present (20:18, 9 September 2018 (UTC)).<br />
<br />
* "'''-pef-'''" for "{{jvs|pe'a}}". -- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 18:44, 10 January 2019 (UTC)<br />
<br />
=== Experimental "-goi-" and "-zoi-" usages ===<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
<br />
This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.<br />
<br />
== See Also ==<br />
<br />
* [[Proposal: "no"-"nu" Transposition]]. The cmavo "no" and "nu" would have their definitions mutually exchanged. The meanings of the rafsi would, therefore, be mutually exchanged as well. However, the forms of the rafsi are not altered.<br />
* [[Proposal: Drag-and-Drop Conversion Becomes Default]]. The meanings of "te" and "to'ai", of "ve" and "vo'ai", and of "xe" and "xo'ai" would each - respectively - be transposed; as such, the proposal also would redefine (but not reassign) the rafsi of each of these words so as to match their new meanings; "se" / "-sel-" would not be affected.<br />
* [[ce ki tau jau]]. Has numerous implications for rafsi, depending on which changes are implemented.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Universal_Extremal-Syllable_Stress&diff=123143Proposal: Universal Extremal-Syllable Stress2018-11-06T03:39:00Z<p>Krtisfranks: Created page with "{{jbocre/en}} Krtisfranks proposes that Lojban be modified so that ''each'' word has mandatory stress on exactly its either first or♠ final syllable, excepting: cmevla (suc..."</p>
<hr />
<div>{{jbocre/en}}<br />
<br />
Krtisfranks proposes that Lojban be modified so that ''each'' word has mandatory stress on exactly its either first or♠ final syllable, excepting: cmevla (such that alternative stress is denoted in written form), words wherein such syllable has only "y" or a syllabic consonant as its nucleus, and other expressions which are demarcated by mandatory "." on either side. Notably, this would apply to cmavo as well as brivla.<br />
<br />
♠ (This 'OR' statement is exclusive-definite: for affected polysyllabic words, the stress would be placed on the either first xor final syllable of said word, each; for monosyllabic words, the stress would be placed on the only syllable present (which is both the first and the final syllable) - in which case, the 'OR' becomes an 'AND').<br />
<br />
<br />
== Benefits ==<br />
<br />
Not all words are polysyllabic, so not all words can be stressed on their penult (because none exists). But all words, excepting the empty string/word, are at-least-monosyllabic and, thus, can be stressed on their either first xor final syllables (each of which is guaranteed to exist; again, note that equivalence of these syllables changes 'XOR' to 'AND').<br />
<br />
Stress would be understood as meaning that a word boundary is 'imminent' in the sense that it either just happened or is about to happen. There is no wait for it.<br />
<br />
Stress would be highly predictable. As it is now, a word can be modified and thereby lose its identifying stress pattern (for example: any CCVCVCV word derived from a CCVCV gismu changes the stress in the gismu from the gismu's first syllable to its last), or two words can be combined into a lujvo such that the same happens. Such would not necessarily happen (depending on the choice of proposal) if this proposal were adopted.<br />
<br />
Morphology would be dramatically freed up. Many disallowed forms would be newly allowed because word boundaries would be less problematic to determine. A lot of the complexities of Lojban's morphological considerations (including things like slinku'i and tosmabru) are do to issues concerning uniquely identifying word boundaries; these issues would be alleviated and such words could be used without consternation or concern.<br />
<br />
This would greatly reduce the complexity (especially for a human during a vocal conversation, in real time) in determining where word breaks occur and whether stress can be placed on a given syllable of a given cmavo in the particular context at hand. It also greatly simplifies the grammar rules regarding stress, which is especially beneficial while teaching newcomers.<br />
* Presently, the grammar allows for free stress on cmavo except in certain circumstances; some have proposed that this exception may itself be deserving of exception (because it is an unnecessary restriction in some cases). However, keeping track of all of these exceptions can be difficult. This rule would eliminate such concerns.<br />
<br />
It should(?) mean that some lujvo simplify in that no hyphen is required. Since word breaks would immediately precede or immediately follow the stressed syllable respectively (depending on which option of this proposal is chosen), rafsi strings which could/would be interpreted as containing cmavo (such as in the current grammar) would be interpreted as belonging to a single word, thereby yielding a lujvo. For example, "ro'ire'o" would be understood as a single word (either "rO'ire'o" xor "ro'ire'O" respectively, depending on proposal option), and so would be the lujvo "rokci zei renro"; the 2-cmavo string "ro'i re'o" would be distinguished from this as having two points of stress, rather than merely one, near word boundaries (namely, "rO'i rE'o" xor "ro'I re'O" respectively, similarly depending).<br />
<br />
== Disadvantage ==<br />
<br />
Words such that the otherwise affected syllable has only "y" or a syllabic consonant as its nucleus would be decomposed oddly. For example: "mlatu krtis" if rendered as "mlAtu krtis" or (worse) "mlAtu krtIs" would be interpreted as "mlAtukrtis" or "mlAtukr tIs" respectively. This might be especially bad for zi'evla with classifier rafsi/terms which are monosyllabic or disyllabic with only "y" or syllabic consonants present in at least the first syllable nucleus.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123066experimental rafsi2018-09-09T20:18:38Z<p>Krtisfranks: /* Proposed and Unofficial */</p>
<hr />
<div>== Introduction and Classification ==<br />
<br />
Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
Additionally, this page tends to focus on individual, atomic, and self-contained proposals which do not have larger effects, proposals, projects, or ideas behind them - with notable exceptions for series (such as for hexadecimal digits, drag-and-drop selbri-conversion, FA, etc.); in time, hopefully, additional discussions which touch on or which would be strongly affected by experimental rafsi can be added or linked to (such as in a "See Also" section).<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
**: Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
***: No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
***: ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-tez-'''" for "{{jvs|te'o}}" also. See: "{{jvs|tezda}}".<br />
** "'''-cix-'''" for "{{jvs|ci'i}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
** "'''-xox-'''" for "{{jvs|xo}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gav-'''" for "{{jvs|grava}}".<br />
* "'''-vul-'''" for "{{jvs|vubla}}".<br />
* "'''-xig-'''" for "{{jvs|xigzo}}".<br />
* "'''-mug-'''" for "{{jvs|mugle}}".<br />
* "'''-xob-'''" for "{{jvs|xonba}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
* "{{jvs|kamre}}" probably could use a cmarafsi too, but I ([[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]])) am not sure what to do for it at present (20:18, 9 September 2018 (UTC)).<br />
<br />
=== Experimental "-goi-" and "-zoi-" usages ===<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
<br />
This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.<br />
<br />
== See Also ==<br />
<br />
* [[Proposal: "no"-"nu" Transposition]]. The cmavo "no" and "nu" would have their definitions mutually exchanged. The meanings of the rafsi would, therefore, be mutually exchanged as well. However, the forms of the rafsi are not altered.<br />
* [[Proposal: Drag-and-Drop Conversion Becomes Default]]. The meanings of "te" and "to'ai", of "ve" and "vo'ai", and of "xe" and "xo'ai" would each - respectively - be transposed; as such, the proposal also would redefine (but not reassign) the rafsi of each of these words so as to match their new meanings; "se" / "-sel-" would not be affected.<br />
* [[ce ki tau jau]]. Has numerous implications for rafsi, depending on which changes are implemented.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123065experimental rafsi2018-09-09T19:57:45Z<p>Krtisfranks: /* See Also */</p>
<hr />
<div>== Introduction and Classification ==<br />
<br />
Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
Additionally, this page tends to focus on individual, atomic, and self-contained proposals which do not have larger effects, proposals, projects, or ideas behind them - with notable exceptions for series (such as for hexadecimal digits, drag-and-drop selbri-conversion, FA, etc.); in time, hopefully, additional discussions which touch on or which would be strongly affected by experimental rafsi can be added or linked to (such as in a "See Also" section).<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
=== Experimental "-goi-" and "-zoi-" usages ===<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
<br />
This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.<br />
<br />
== See Also ==<br />
<br />
* [[Proposal: "no"-"nu" Transposition]]. The cmavo "no" and "nu" would have their definitions mutually exchanged. The meanings of the rafsi would, therefore, be mutually exchanged as well. However, the forms of the rafsi are not altered.<br />
* [[Proposal: Drag-and-Drop Conversion Becomes Default]]. The meanings of "te" and "to'ai", of "ve" and "vo'ai", and of "xe" and "xo'ai" would each - respectively - be transposed; as such, the proposal also would redefine (but not reassign) the rafsi of each of these words so as to match their new meanings; "se" / "-sel-" would not be affected.<br />
* [[ce ki tau jau]]. Has numerous implications for rafsi, depending on which changes are implemented.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123064experimental rafsi2018-09-09T19:48:20Z<p>Krtisfranks: /* Table of all Experimental rafsi which appear on this page */</p>
<hr />
<div>== Introduction and Classification ==<br />
<br />
Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
Additionally, this page tends to focus on individual, atomic, and self-contained proposals which do not have larger effects, proposals, projects, or ideas behind them - with notable exceptions for series (such as for hexadecimal digits, drag-and-drop selbri-conversion, FA, etc.); in time, hopefully, additional discussions which touch on or which would be strongly affected by experimental rafsi can be added or linked to (such as in a "See Also" section).<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
=== Experimental "-goi-" and "-zoi-" usages ===<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
<br />
This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.<br />
<br />
== See Also ==<br />
<br />
* [[Proposal: "no"-"nu" Transposition]]. The cmavo "no" and "nu" would have their definitions mutually exchanged. The meanings of the rafsi would, therefore, be mutually exchanged as well. However, the forms of the rafsi are not altered.<br />
* [[Proposal: Drag-and-Drop Conversion Becomes Default]].</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123063experimental rafsi2018-09-09T19:42:30Z<p>Krtisfranks: </p>
<hr />
<div>== Introduction and Classification ==<br />
<br />
Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
Additionally, this page tends to focus on individual, atomic, and self-contained proposals which do not have larger effects, proposals, projects, or ideas behind them - with notable exceptions for series (such as for hexadecimal digits, drag-and-drop selbri-conversion, FA, etc.); in time, hopefully, additional discussions which touch on or which would be strongly affected by experimental rafsi can be added or linked to (such as in a "See Also" section).<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
=== Experimental "-goi-" and "-zoi-" usages ===<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
<br />
This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Great_Rafsi_Reallocation&diff=123062Great Rafsi Reallocation2018-09-09T19:34:15Z<p>Krtisfranks: Redirected page to the Great Rafsi Reallocation</p>
<hr />
<div>#REDIRECT [[the Great Rafsi Reallocation]]</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Drag-and-Drop_Conversion_Becomes_Default&diff=123061Proposal: Drag-and-Drop Conversion Becomes Default2018-09-09T19:31:04Z<p>Krtisfranks: </p>
<hr />
<div>The idea would be to redefine:<br />
* new-"te" so as to mean old-"{{jvs|to'ai}}", and new-"to'ai" so as to mean old-"te";<br />
** Thus, if this proposal were to be adopted (so all words would have their new meanings) and<br />
**: if the original selbri had its sumti slots ordered as: x1 x2 x3 x4 x5 ..., then:<br />
**: "te" would drag-and-drop the third sumti slot to the first position, resulting in ordering: x3 x1 x2 x4 x5 ...;<br />
**: and "to'ai" would transpose the third and first sumti slot with one another, resulting in ordering: x3 x2 x1 x4 x5 ...<br />
* new-"ve" so as to mean old-"{{jvs|vo'ai}}", and new-"vo'ai" so as to mean old-"ve";<br />
* new-"xe" so as to mean old-"{{jvs|xo'ai}}", and new-"xo'ai" so as to mean old-"xe".<br />
Additionally:<br />
* "se" would be unaffected.<br />
* The rafsi would remain associated with the word/word form/string with which they share their first vowels, so their meanings would be redefined (but their assignment wrt word/word form/string would be unchanged).<br />
** Thus, for example: new-"-ter-" would be assigned to new-"te" and would mean old-"to'ai"/old-"-toz-" (if that rafsi is accepted); new-"-toz-" would be assigned to new-"to'ai" and would mean old-"te"/old-"-ter-". Etc. for the other conversions. As such:<br />
**: "terbroda" would decompose to "te broda" and would have ordering: x3 x1 x2 x4 x5 ...;<br />
**: meanwhile, "tozbroda" would decompose to "to'ai broda" and would have ordering: x3 x2 x1 x4 x5 ...<br />
*** If the rafsi for "te" becomes "-tel-", then exchange "-ter-" with "-tel-" throughout this example.<br />
** Therefore, "-sel-" (assigned to "se") would be unaffected.<br />
<br />
<br />
This would require a substantial reworking of lujvo.<br />
<br />
It might be worth it, though, if we feel that drag-and-drop conversion is easier/requires less brain-power or is more natural. Note that rafsi ending in "l" or "r" are more coveted than those which end in "z".</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Drag-and-Drop_Conversion_Becomes_Default&diff=123060Proposal: Drag-and-Drop Conversion Becomes Default2018-09-09T19:28:26Z<p>Krtisfranks: </p>
<hr />
<div>The idea would be to redefine:<br />
* new-"te" so as to mean old-"{{jvs|to'ai}}", and new-"to'ai" so as to mean old-"te";<br />
** Thus, if this proposal were to be adopted (so all words would have their new meanings) and<br />
**: if the original selbri had its sumti slots ordered as: x1 x2 x3 x4 x5 ..., then:<br />
**: "te" would drag-and-drop the third sumti slot to the first position, resulting in ordering: x3 x1 x2 x4 x5 ...;<br />
**: and "to'ai" would transpose the third and first sumti slot with one another, resulting in ordering: x3 x2 x1 x4 x5 ...<br />
* new-"ve" so as to mean old-"{{jvs|vo'ai}}", and new-"vo'ai" so as to mean old-"ve";<br />
* new-"xe" so as to mean old-"{{jvs|xo'ai}}", and new-"xo'ai" so as to mean old-"xe".<br />
* "se" would be unaffected.<br />
* The rafsi would remain associated with the word/word form/string with which they share their first vowels, so their meanings would be redefined (but their assignment wrt word/word form/string would be unchanged).<br />
** Thus, for example: new-"-ter-" would be assigned to new-"te" and would mean old-"to'ai"/old-"-toz-" (if that rafsi is accepted); new-"-toz-" would be assigned to new-"to'ai" and would mean old-"te"/old-"-ter-". Etc.<br />
**: "terbroda" would decompose to "te broda" and would have ordering: x3 x1 x2 x4 x5 ...;<br />
**: meanwhile, "tozbroda" would decompose to "to'ai broda" and would have ordering: x3 x2 x1 x4 x5 ...<br />
*** If the rafsi for "te" becomes "-tel-", then exchange "-ter-" with "-tel-" throughout this example.<br />
<br />
<br />
This would require a substantial reworking of lujvo.<br />
<br />
It might be worth it, though, if we feel that drag-and-drop conversion is easier/requires less brain-power or is more natural. Note that rafsi ending in "l" or "r" are more coveted than those which end in "z".</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123059experimental rafsi2018-09-09T19:19:16Z<p>Krtisfranks: Organized page</p>
<hr />
<div>Experimental rafsi are rafsi which are:<br />
* Class #1: proposed to be assigned to a word by an individual or the community, but which have not been officially accepted (and which have no other current or prior assignment which is considered to be official); or<br />
* Class #2:<br />
**: Class #2a: used in non-official or non-standard ways<br />
**: Class #2b: the result of de-assignment or re-assignment from words to which they were officially assigned.<br />
<br />
For the purposes of this definition/classification: Official rafsi (or their assignments) are necessarily those which were published as such, by the appropriate authority, ''after'' the [[Great Rafsi Reallocation]].<br />
<br />
Technically, any experimental gismu automatically has two experimental {{jvs|brarafsi}} assigned to it: itself, and itself without the final vowel. Likewise, under some schemes, all {{jvs|zevla}} have at least one experimental rafsi: themselves; they may also have more according to scheme. This page is not concerned with any of these. Instead, it focuses on experimental {{jvs|cmarafsi}} of (potentially experimental) gismu and sometimes zevla, as well as experimental (cma)rafsi for (possibly experimental) cmavo.<br />
<br />
== Mostly-Official rafsi ==<br />
<br />
These might be on certain official lists or may be mentioned in the [[CLL]]. They just may not appear in all such lists or might have some other discrepancies. These ones are essentially official and should be universally understood without too much issue or contest.<br />
<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
<br />
== Proposed and Unofficial ==<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
=== Experimental "-goi-" and "-zoi-" usages ===<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
== Table of all Experimental rafsi which appear on this page ==<br />
<br />
The following will be a table of a subset of the proposed rafsi which appear on this page. It shall be organized alphabetically by at least rafsi and shall have columns: (proposed rafsi, proposed assigned word, experimental rafsi class (per top of this page), category to which the associated word belongs (gismu/cmavo), conflicts, notes).<br />
<br />
This table will be a subset of the proposals which appear on this page. For more information or for related proposals, check out the associated proposal. Additionally, some proposals or information may be missing from the table, even if it appears elsewhere on this page; always check (Ctrl+F) the entire page for a potential rafsi, not just the table - add any errors which you find.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123058experimental rafsi2018-09-09T18:45:51Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-rex-'''" for "{{jvs|rexsa}}".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
____<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
____</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123057experimental rafsi2018-09-09T18:37:24Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**{{jvs|xei}} rafsi: xem<br />
*** See: [[xei]].<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}".<br />
* "'''-gul-'''" for "{{jvs|gugle}}".<br />
* "'''-vaf-'''" for "{{jvs|valfa}}".<br />
* "'''-zic-'''" for "{{jvs|zmico}}".<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").<br />
<br />
____<br />
<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
<br />
____</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123056experimental rafsi2018-09-09T18:13:00Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo {{jvs|rexsa}} .i oiro'a<br />
<br />
*[[Krtisfranks]]:<br />
*:Other numbers/digits:<br />
** "'''-tex-'''" for "{{jvs|te'o}}".<br />
** "'''-xix-'''" for "{{jvs|xi}}".<br />
** "'''-xon-'''" for "{{jvs|xo'ei}}".<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}"<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Drag-and-Drop_Conversion_Becomes_Default&diff=123055Proposal: Drag-and-Drop Conversion Becomes Default2018-09-09T17:27:07Z<p>Krtisfranks: Created page with "The idea would be to redefine: * new-"te" to mean old-"{{jvs|to'ai}}", and new-"to'ai" to mean old-"te"; * new-"ve" to mean old-"{{jvs|vo'ai}}", and new-"vo'ai" to mean old-"v..."</p>
<hr />
<div>The idea would be to redefine:<br />
* new-"te" to mean old-"{{jvs|to'ai}}", and new-"to'ai" to mean old-"te";<br />
* new-"ve" to mean old-"{{jvs|vo'ai}}", and new-"vo'ai" to mean old-"ve";<br />
* new-"xe" to mean old-"{{jvs|xo'ai}}", and new-"xo'ai" to mean old-"xe".<br />
* "se" would be unaffected.<br />
* The rafsi would remain associated with the word/word form/string with which they share the first vowels, so their meanings would be redefined (but their assignment wrt word form/string would be unchanged).<br />
** Thus, for example: new-"-ter-" would be assigned to new-"te" and would mean old-"to'ai"/old-"-toz-" (if that rafsi is accepted); new-"-toz-" would be assigned to new-"to'ai" and would mean old-"te"/old-"-ter-". Etc.<br />
*** If the rafsi for "te" becomes "-tel-", then exchange "-ter-" with "-tel-" throughout this example.<br />
<br />
<br />
This would require a substantial reworking of lujvo.<br />
<br />
It might be worth it, though, if we feel that drag-and-drop conversion is easier/requires less brain-power or is more natural. Note that rafsi ending in "l" or "r" are more coveted than those which end in "z".</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123054experimental rafsi2018-09-09T17:14:59Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
* "'''-tex-'''" for "{{jvs|te'o}}".<br />
* "'''-xix-'''" for "{{jvs|xi}}".<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}"<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123053experimental rafsi2018-09-09T06:59:57Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
** "-jiv-" is more desirable because of the otherwise general pattern for selma'o JA.<br />
*** Proposal: First, make "jn" become a permissible initial consonant cluster. Second, unassign all current rafsi of "{{jvs|jinvi}}" (this is overkill, but we might as well do it right if we do it at all). Then, assign "-jni-" to "jinvi", and "-jiv-" to "ji" (regardless of assignment/retention or non-assignment/loss of "-jix-" for the same).<br />
* "'''-tex-'''" for "{{jvs|te'o}}".<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}"<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123052experimental rafsi2018-09-09T06:50:48Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{{jvs|nai}}". (Read additional commentary there).<br />
** Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi for this word, at any given time.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
* "'''-tex-'''" for "{{jvs|te'o}}".<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}"<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123051experimental rafsi2018-09-09T06:48:31Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
* "'''-niz-'''" or "'''-nij-'''" for "{jvs|nai}". (Read additional commentary there). Possibly reässign "'''-nai-'''" or "'''-nax-'''" to "nai"; select no more than three rafsi.<br />
* "'''-jix-'''" for "{{jvs|ji}}".<br />
* "'''-tex-'''" for "{{jvs|te'o}}".<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-nif-'''" for "{{jvs|nicfa}}"<br />
* Angular directions:<br />
** "'''-zu'a-'''" for "{{jvs|zucna}}",<br />
** "'''-tso-'''" for "{{jvs|dutso}}";<br />
** "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123027experimental rafsi2018-08-31T03:14:53Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-coc-'''" for "{{jvs|corci}}".<br />
* "'''-zu'a-'''" for "{{jvs|zucna}}", and "'''-tso-'''" for "{{jvs|dutso}}"; "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123026experimental rafsi2018-08-31T03:12:52Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi/Tsani (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi/Tsani proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-zu'a-'''" for "{{jvs|zucna}}", and "'''-tso-'''" for "{{jvs|dutso}}"; "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123025experimental rafsi2018-08-31T03:08:16Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
*Proposed at http://selpahi.weebly.com/archive/a-list-of-new-rafsi by Selpahi (endorsed by Krtisfranks):<br />
** "{{jvs|fa}} rafsi: "'''-faf-'''".<br />
** "{{jvs|fe}} rafsi: "'''-fef-'''".<br />
** "{{jvs|fi}} rafsi: "'''-fif-'''".<br />
** "{{jvs|fo}} rafsi: "'''-fof-'''".<br />
** "{{jvs|fu}} rafsi: "'''-fuf-'''".<br />
*** (Not technically proposed by Selpahi, but that was probably just an oversight)<br />
** "{{jvs|fai}} rafsi: "'''-fox-'''".<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-pom-'''" or "'''-pov-'''" for "{{jvs|po'o}}".<br />
** Selpahi proposed "-pov-"; Krtisfranks proposed "-pom-". "-pom-" has a higher chance of combining in a more compact form because "v" cannot be immediately followed by "v" or a voiceless letteral, whereas "m" can be immediately followed by any consonant except "m".<br />
* "'''-zu'a-'''" for "{{jvs|zucna}}", and "'''-tso-'''" for "{{jvs|dutso}}"; "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123024experimental rafsi2018-08-31T02:54:51Z<p>Krtisfranks: copy-editing/typesetting</p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-zu'a-'''" for "{{jvs|zucna}}", and "'''-tso-'''" for "{{jvs|dutso}}"; "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123023experimental rafsi2018-08-31T02:49:03Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
** This one is essentially official.<br />
<br />
<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rafsi zo {{jvs|ditcu}}<br />
* "'''-sus-'''" for "{{jvs|smusu}}".<br />
* "'''-sem-'''" for "{{jvs|su'ei}}".<br />
* "'''-zve-'''" for "{{jvs|zevla}}".<br />
* Drag-and-drop selbri conversion series:<br />
** "'''-toz-'''" for "{{jvs|to'ai}}".<br />
<br />
** "'''-voz-'''" for "{{jvs|vo'ai}}".<br />
<br />
** "'''-xoz-'''" for "{{jvs|xo'ai}}".<br />
* "'''-zu'a-'''" for "{{jvs|zucna}}", and "'''-tso-'''" for "{{jvs|dutso}}"; "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=experimental_rafsi&diff=123022experimental rafsi2018-08-31T01:27:45Z<p>Krtisfranks: </p>
<hr />
<div>aka "[[rafsi]] not in the official lists" (some are mentioned in [[CLL]], though).<br />
*{{jvs|jai}} rafsi: '''jax''', '''jaz'''<br />
*{{jvs|nei}} rafsi: '''nej'''<br />
*{{jvs|zi'o}} rafsi: '''zil''' (in the gismu list, just not the rafsi list)<br />
*{{jvs|kibro}} rafsi: '''kib''' (experimental gismu)<br />
<br />
*[[rab.spir|rab.spir]]:<br />
*:I suggest these for hex digits:<br />
**{{jvs|dau}} rafsi: duv<br />
**{{jvs|fei}} rafsi: fel<br />
**{{jvs|gai}} rafsi: gam<br />
**{{jvs|jau}} rafsi: juz<br />
**[[xei]] rafsi: xem<br />
**{{jvs|vai}} rafsi: vav<br />
<br />
*[[Adam|Adam]]:<br />
*:{{jvs|rei}} rafsi: rex (for those who don't see the need for [[xei|xei]])<br />
** Or just say that xem is a rafsi for xei or rei, whichever you use.<br />
*** No other cmavo has a rafsi whose only similarity to it is the vowel.<br />
*** ku'i ra'oi -rex- ca jai se djica fai tu'a zo rexsa .i oiro'a<br />
<br />
coi doi ro do mi'e .telselkik. .i .u'u mi co'a rafsypli<br />
.i du'e jbopre pu pante lo za'i lo rafsi cu na'e xamgu kei mi<br />
lo drata be lo nu sampu zbasu lo xamgu lo na'e selpli rafsi<br />
.i .ai .au co'a cikre .i ko xendo bi'a sidju .au<br />
<br />
* .i zo {{jvs|selja'e}} se rafsi ti'e ra'oi '''se'e''' (to mi mi'e .tel. na'e finti .i milxe laldo ca .i racli pe'i .i .ei sai lo nu na'e satci cu banzu frili bau la ma'a melbau toi)<br />
* .i zo {{jvs|mu'umgu}} se rafsi ca'e ra'oi '''mug''' (to mi sezysarxe li'a mu'umgu ra'oi '''mug''' lo nu mugyta'a kei lo jbopre toi)<br />
* .i ra'oi '''zmo''' zo'u: ''fabu'' pilno ''febu'' lo nu ''febu'' jai stika lo ka ''fabu'' lifri ma kau kei lo mutce .i fanva zo'oi ''high'' .e zo'oi ''intoxicated'' .e zo'oi ''entranced'' (to no da ca se rafsi .i ku'i cumki li'a fa lo nu finti lo jitfa krasi zi'evla toi)<br />
** pe'i .ei sai ro gu'e se valsi be fi zo'e gi smuni cu se brivla da .i se ki'u bo tu'e ca'e zo {{jvs|zmo'una}} se rafsi zo'oi. zmo. tu'u .i ko va'o lo nu na nelci cu jai stika<br />
* .i ra'oi '''bom''' .e ra'oi '''nom''' .i srana lo nu pilno lo rafsi pe lo jvocme lo nu zbasu lo lujvo .i ka'u ma'a cafne je zasni je xalbo finti lo simsa .i zo xorxesyjbo cu mupli .i la selpa'i ku noi banli cu pilno ti'e (to mi korpora zei sisku mupli facki toi) .i li'a tavla fi la .xorxes. noi ji'a banli .i na li'a tavla fi lo xelso mu'a .i ku'i malrarbausmi relsmununrafpli .i to'e jbosarxe pe'i .i ro ma'a djuno lo du'u na'e jbosarxe .i ma'a mu'i pilno fi lo se xalbo po'o .i ku'i xamgu sidbo pe'i .i pe'i xlali tadji po'o .i .ei satci .i mi mu'i finti ra'oi '''bom''' .e ra'oi '''nom''' .i to'u zo xorxesyjbo cu binxo zo xorxesnomjbo .i ra'oi '''bom''' cu se pilno fi lo nu cmene lidne ke zmadu ciksi .i mu'a lu zabna me la .xorxes. me'u lojbo li'u cu ve lujvo fo zo zanbomxorxesnomjbo .i ca'e ru'e .ia ru'e lu lo combomcmevla li'u mu'a cu panra lu lo co'e do'e la cmevla li'u .i .ia sai .o'a plixautce ciste .i .au pilno lo na'e purselpli rafsi lo banzu xamgu .i xamgu pe'i fa lo nu kargau pe'a lo cnino poi vlaca'u .i zmadu vrici pilno lo zasti rafsi .ui poi sormei .i mutce prali .i .a'o do tugni .i va'i .a'o do nelci lo cizbomselkiknomsi'o doi jbope'o mi'e la stela selckiku mu'o pante<br />
** Translated summary: '''-bom-''' and '''-nom-''' are proposed rafsi for "start of name" and "end of name" respectively, which may be useful for lujvo involving [[brivycme]]<br />
* .i ra'oi '''ne'a''' rafsi ca'e zo bebna .i zo bebna cu cafne se pilno fi lo valsi fanmo .i ku'i lo mapti poi rafsi cu selpli fi no da .i pu malne'a pe'i<br />
<br />
zai ze'ei coi jbope'o mi'e .telselkik.<br />
.i mi ca'o rafsyxaksygau<br />
.i ji'a lo drata cu co'a sidju<br />
.i ji'a mi jajgau lo laldo se finti ti poi .uitki<br />
.i .a'o ro do plitce<br />
<br />
* .i ra'oi '''-xro-''' rafsi zo xrotu<br />
* .i ra'oi '''-glo-''' rafsi zo glotu<br />
* .i ra'oi '''-xlo-''' rafsi zo xlotu<br />
* .i ra'oi '''-va'a-''' rafsi zo va'arga<br />
* .i ra'oi '''-zvi-''' rafsi zo zviki noi la ramcinfo ca'o finti (provisional definition: x1 participates in co-creative act x2 in context of system x3 inspired/allowed by its quality x4; x1 hacks x3 exploiting x4 (x2 being the hack))<br />
* .i la danmo rozgu cu gasnu lo nu ra'oi '''-jbo-''' co'u rafsi zo lojbo je cu co'a rafsi zo jbobo (to ku'i smudu'i toi)<br />
* .i la .niftyg. cu gasnu lo nu ra'oi '''-bob-''' ji'a cu srana lo si'o bobyjbobylobybobyjbojbobylojbo .i mi finti zo bo'objo noi jitfykrasi<br />
* .i ra'oi '''-vob-''' rafsi zo vo'a si'au (to zo vobmipri co'e toi)<br />
* .i li'a ra'oi '''-goi-''' je ra'oi '''-zoi-''' vaitce .i no drata simsa tordu je cu nu'o selpli .i pe'i no cmalu smuni cu mapti .i .e'u srana lo nu zbasu lo bramau poi canlu .i ra'oi '''-goi-''' cu ca'e co'e lo kulnu rafsi .i za'a so'i prenu cu xebni lo kulnu rafsi .i na'e jbosarxe .i to'e klunu'i .i na'e cumki fa lo nu ro remna kulnu cu co'e lo tordu rafsi .i ku'i nandu fa lo nu gasnu lo nu lo zasti poi kulnu rafsi cu co'u se pilno .i mi ca troci lo nu ba'e ''muvdu'' .i ra'oi '''-mer-''' pu rafsi zo merko .i ra'oi '''-mergoi-''' ca'e co'a rafsi zo merko .i zo merpre binxo zo mergoipre .i da'i sai! ba lo ba zu nu ra'oi '''-mer-''' poi lunbe cu co'u pilno fi tu'a zo merko kei cu co'a xamgu fa lo nu pilno ra'oi '''-mer-''' lo drata .i zmadu vajni fa lo za'i kakne lo nu finti lo klunu'i dunli clani rafsi be do'e lo vrici poi kulnu je poi jbovla tu'a ki fa lo po'o na'e gismu .i ra'oi '''-zoi-''' simsa ca'e je cu srana lo ku'i zifre canlu .i mu'a ra'oi '''-vanzoi-''' rafsi zo vanlamigu .i zo vanzoizga mu'a lujvo fo lu vanlamigu zgana li'u .i cizra .ie nai pei fa lo da'i nu lo fadni tordu cu rafsi zo vanlamigu .i mu'i finti lo sarxe barda poi cnino je poi rafsi canlu<br />
** Translated summary: '''-goi-''' is a proposed special rafsi, modifying the previous rafsi to indicate "cultural rafsi". This allows rafsi with existing assignments to also be assigned to a culture, giving more space for each major culture to get a rafsi. e.g. '''-sfegoi-''' might be able to represent '''sfe'ero''' (Swedish), despite '''-sfe-''' already being assigned to '''sefta'''. In another part of this proposal, existing cultural rafsi will also be reassigned to also use '''-goi-''', so as to be more culturally neutral.<br />
*** Additional note; hm, this also allows '''sfegoi''', '''mergoi''' etc. to be proper brivla in their own right...<br />
*** [[User:Spheniscine|Spheniscine]] ([[User talk:Spheniscine|talk]]) 02:01, 14 djulio 2015 (PDT) Just for fun (not sure if I'd actually use them), I'm going to list possible -goi- assignments for existing cultural words. Some (marked with asterisks) will use a different rafsi than what they were assigned, so as to avoid having to use a hyphen; I, however, completely ignored and disavow any associations with what the rafsi might already be assigned to:<br />
**** jungo → jungoi*<br />
**** glico → gligoi<br />
**** xindo → xingoi<br />
**** spano → sangoi<br />
**** rusko → ruzgoi*<br />
**** xrabo → rabgoi<br />
**** bengo → bengoi*<br />
**** porto → porgoi*<br />
**** baxso → bazgoi*<br />
**** ponjo → pongoi<br />
**** dotco → dojgoi*<br />
**** fraso → fragoi*<br />
**** xurdo → xurgoi<br />
**** merko → mergoi<br />
**** brito → brigoi*<br />
**** skoto → skogoi*<br />
**** sralo → sragoi*<br />
**** kadno → kadgoi*<br />
**** gento → gengoi*<br />
**** mexno → mengoi*<br />
**** softo → sovgoi*<br />
**** vukro → vurgoi<br />
**** filso → filgoi*<br />
**** jerxo → jergoi*<br />
**** jordo → jorgoi<br />
**** libjo → libgoi<br />
**** lubno → lungoi*<br />
**** misro → mizgoi*<br />
**** morko → morgoi<br />
**** rakso → rajgoi*<br />
**** sadjo → djogoi<br />
**** sirxo → sirgoi*<br />
**** bindo → bidgoi<br />
**** meljo → mejgoi<br />
**** brazo → razgoi<br />
**** kisto → kizgoi*<br />
**** -skip the continent ones; those are probably fine as is-<br />
**** latmo → lamgoi*<br />
**** srito → srigoi*<br />
**** xebro → xebgoi<br />
**** xelso → xelgoi*<br />
**** budjo → bujgoi<br />
**** dadjo → dajgoi<br />
**** muslo → muzgoi*<br />
**** xriso → xrigoi*<br />
**** jegvo → jevgoi*<br />
**** semto → smegoi<br />
**** slovo → lovgoi<br />
**** xispo → xizgoi*<br />
** '''-zoi-''' is proposed to modify the previous rafsi to indicate "free rafsi", being able to represent any word that is suitably mnemonic. E.g. '''-vanzoi-''' might represent '''vanlamigu''' or '''vandula''' or '''vandani'''; all depends on how the resulting lujvo is defined. (.y .ie nai .i mi na tugni lo lidne bangenugu bo selsku (uh, no. i disagree with the preceding english statement.) .i .ai lo ra'oi -zoi- rafsi cu se pilno fi po stodi rafsi lo steci (i intend that -zoi- be used to steadily be the rafsi of something in particular.) .i mu'a ra'oi -vanzoi- rafsi ca'e .ai zo vanlamigu po'o (for instance -vanzoi- i'm declaring to be a rafsi for {vanlamigu} only.) .i .u'u cfipu (sorry about the confusion.) mu'o mi'e .tel. (cya i'm stela selckiku))<br />
* '''-zam-''' is proposed as the rafsi of '''zai'e''', indicating a jargon word. It is proposed that lujvo ''beginning'' with '''-zam-''' should be free for assignment by any context that may need a jargon word, either through contextual explanation or by explicit assignment with '''cei'''. Lujvo ''containing'' '''-zam-''' (and possibly lujvo in the form of "'''<cmevla> zei zambroda'''") may be defined with a particular meaning in JVS to "trickle down" a jargon word into common usage, e.g. hypothetical Lojbanic engineers working on the first computers might first call the computer mouse '''zamsmacu''', which becomes '''samyzamsmacu''' when computers become mainstream, which then possibly becomes '''samsmacu''' after high frequency usage (in reality though, the computer mouse is assigned to '''pevysmacu''' and '''sma'acu''')<br />
* .i ti'e ra'oi '''-jos-''' rafsi zo {{jvs|jonse}}<br />
* .i ti'e ra'oi '''-dit-''' rasi zo {{jvs|ditcu}}<br />
* "'''-zu'a-'''" for "{{jvs|zucna}}", and "'''-tso-'''" for "{{jvs|dutso}}"; "zn" becomes a permissible initial consonant cluster iff "'''-zna-'''" is assigned as a rafsi to "zucna" as well (or possibly instead of "-zu'a-").</div>Krtisfrankshttps://mw.lojban.org/index.php?title=lo_jboce%27u_selzukseltcuste_pe_la_2017_gregOriiys_nanca&diff=122755lo jboce'u selzukseltcuste pe la 2017 gregOriiys nanca2018-04-17T20:13:18Z<p>Krtisfranks: </p>
<hr />
<div>This is an informal list of problems and possible solutions (and the accompanying considerations) compiled on behalf of the Lojban community by lai .krtisfranks. and submitted to the LLG in A.D. 2017.<br />
<br />
<br />
== Desires/Goals ==<br />
* Lojban community that does “lots of translations and projects and such”.<br />
* Develop a more active, less random arrangement of independent endeavors.<br />
* Need a place/way to inform others of such projects. Outreach is presently problematic.<br />
* Organize the main website better. Separate out official stuff from unofficial stuff. Possibly put things into<br />
each user’s personal space if it is unofficial.<br />
* Reduce learning curve for joining community<br />
* Build a tighter, more organized, more self-aware community<br />
* Develop goals for language exploration/projects.<br />
* Retain people<br />
* Sponsor certain works so that others may see them. Keep the styles, formats, difficulties, and lengths<br />
diverse. Experiencing other people’s works will encourage people to stay with it and to contribute<br />
themselves; having one’s work appreciated will encourage one to produce more and to stay involved.<br />
<br />
== Methods ==<br />
* Community round-up ( https://solpahi.wordpress.com/2017/01/30/monthly-lojban- community-roundup-<br />
january-2017/ )<br />
** Advertise it. Endorse it?<br />
* Place where people can volunteer in others’ projects.<br />
** Byline/motivational quote: “Most projects could be completed within a few days or weeks if every<br />
Lojbanist wrote one line of Lojban/English every day.”<br />
* Possibly institute a monetary reward for vetted contributions of significance and merit (but allow them to<br />
be small in order to encourage participation).<br />
** Could give a reward to a randomly selected contributor each unit of time. (How would each<br />
contributor’s probability of being selected be determined?)<br />
** Or set up a bounty system: Have a board which specifies a goal/request, the conditions under<br />
which it would be met, and the reward. First person to succeed claims the bounty and it gets<br />
closed and archived.<br />
** Set up an auction. People bid on getting help or contributions/promises vie for reward.<br />
** Possible tasks: contributing translations, learning material/courses/video lectures, updating old<br />
material, cataloguing development or ideas, designing new interfaces/websites, holding<br />
community meet-ups or events, holding advertisement conferences to bring people in, flashcards,<br />
translating common interfaces (programs on phones, etc.), stories, poems, diary entries, captions<br />
for movies or television shows.<br />
** The condition would be that all work submitted would be with the CC0 content licence or similar.<br />
** Negatives:<br />
*** No contract. Could be problematic (legally or just socially – social harm could really<br />
wound our community)<br />
*** How does one determine what is fair? How do we measure work? Poor workers/work<br />
could be rewarded as much as good workers/work. Do we want to encourage<br />
participation and improvement, or do we want to generate good products?<br />
*** Requires large monetary resources.<br />
*** If money disappears, then so too will the interest.<br />
*** Possibly irrevocably alters the character of our community. Is it a community that loves a<br />
great language and wants it to succeed, or is it a business with workers who just want to<br />
make money and do not care about the product or what it means (the wider language) –<br />
and who do as little as possible while still earning it? Is this a translation factory in which<br />
every employee competes against everyone else, or a collaborative exploration of a<br />
common interest?<br />
*** Periodic Nobel-Prize-style, fixed-amount rewards from LLG coffers. Various categories;<br />
review committee; notable/best contributions rewarded.<br />
* Website ideas (a lot of this is from la .timoteios. and la .uakci):<br />
** The website should host only the official or endorsed parts and projects of Lojban.<br />
<br />
** Organize projects centrally via a web-based project-management tool.<br />
*** Perhaps: Phabricator (already used for a Lojban Speech Recognition Tool)<br />
*** Set up http://projects.lojban.org with it.<br />
*** Can also review content. Keeps things organized, centralized, official, and of<br />
quality.<br />
*** Useful for proofreading and providing direct feedback with each item.<br />
*** Can be integrated with Git and shared on GitHub. Can host CLL project.<br />
<br />
** Lojban’s web presence is confusing. What is official? What is archived? What is redundant? What<br />
is deprecated or obsolete? How can one find material about X / What is supposed to be read? How<br />
does one find advice about common topics?<br />
*** Disorganization may be due to the main website being a wiki. Anyone can add anything<br />
and it gets haphazard because no-one is designated to oversee everything.<br />
External/personal websites or alternatives, as well as forums, leave a sprawling mess.<br />
** Maintain a single, central, organized website in which everything is official and code-reviewed<br />
and reviewed by an official committee.<br />
** Make sure that all official material is translated into every main language and that any change in<br />
any of them is propagated/updated in every other version so that everything is maintained together<br />
with only one version of anything (expressed in multiple languages).<br />
** Move the current website to a new website ( wiki.lojban.org ) and link to it from the new main<br />
website with the warning that none of its content should be taken as official unless it is designated<br />
as such on the new main website.<br />
** Would need explicitly defined design goals for the website.<br />
*** Should advertise Lojban effective<br />
*** Provide accessible, up-to- date resources for Lojban (learning, usage, etc.) in all target<br />
languages.<br />
*** Clarify exactly what is official and the status/type of unofficial things.<br />
*** Function as a centralized nexus for the community.<br />
*** Invite involvement from community.<br />
*** Connect Lojbanists.<br />
*** Incorporate/mention all external Lojbanic websites, groups, blogs, etc.<br />
*** Facilitate community projects (and the reward system).<br />
*** Low cognitive barrier-to- entry<br />
*** Work well on desktop and mobile devices.<br />
*** Publish new content only upon the approval of certain people and other conditions.<br />
** Use a system which enables or automates protocols and workflows. Use software with a strict<br />
workflow.<br />
*** Wiki fails here.<br />
** Vocaroo for short audio recordings<br />
** Using the Jekyll static website generator with a plugin to support multiple languages:<br />
*** https://jekyllrb.com/<br />
*** https://github.com/Anthony-Gaudino/jekyll- multiple-languages- plugin<br />
** .PO files being a popular, open-source format for translations<br />
** Could be a plain HTML site which constantly synchronizes with a GitHub repository which in<br />
turn is connected to a workflow organization utility.<br />
*** HTML may alienate non-web- developers. Perhaps use Markdown instead? Would<br />
separate the text from the website structure – allows for manageability and translation<br />
ease.<br />
*** Suggestion for workflow organization utility: Phabricator.<br />
**** No need for GitHub accounts.<br />
**** GitHub has a high learning curve. Phabricator may be more intuitive – need to<br />
trial it.<br />
**** Phabricator is open source. Could customize it. (Translate it to Lojban?)<br />
**** Can automate rebuilding of the static site when changes/new content is<br />
introduced.<br />
**** Might be able to automate the deployment of many Lojban projects (CLL?).<br />
* Expand our community demographically in order to ensure that everything is translated and actively<br />
maintained in as many languages as possible in a translinguistically compatible way.<br />
* Find support for hosting costs.<br />
* List of some projects:<br />
** Tweet things in Lojban (including haikus)<br />
** Write poems.<br />
*** Weekly poems (pemkarni) – an ongoing effort<br />
** Answer Quora questions<br />
** Develop the Interactive Story (lo lisri pe la .norman.)<br />
** Catalogue open questions/problems/topics of exploration<br />
** Lojban Stack Exchange<br />
** Create YouTube vocab-builder slideshows.<br />
** Translate short works. (Perhaps focus on children’s literature or historically important missives).<br />
** Audio record Lojban speech in order to practice and so that others may test recognition.\<br />
** Translate important texts (Bible, etc.)<br />
** Word database<br />
*** Improve/new Anki flashcard decks<br />
*** Organize example sentences for words in one location (per word) with really good<br />
glosses and other notes.<br />
*** Organize lists of lujvo by veljvo.<br />
*** Organize gismu according to frame or the types and case roles of the sumti places.<br />
*** Organize words by frequency.<br />
*** Organize words by topic or meaning (thesaurus).<br />
** Fix sutysisku so that it works offline and does not lose its cache in Firefox.<br />
** Allow for manipulation of dictionaries and texts.<br />
*** Example: First use of a word in a text will have a gloss pop up.<br />
** Maintain list of all words of a certain type without definitions (all gismu-form words, official<br />
gismu, experimental gismu, gismu of form CCVCV, rafsi of form CVV, etc.). This will allow<br />
people to be able to easily access wordlists for programs.<br />
** Maintain a list of rafsi and their associated gismu (and example lujvo?)<br />
** “Designing rules for using terminators that require no software support to apply and that are<br />
learnable, grammatically correct, and reasonably terse. Ku will be scarce, beho more frequent.”<br />
** Figuring out how to write math with mostly bridi and few mekso, based on Robin&#39;s helpful article.<br />
** “Sketching what the language specifications and requirements must have been to come up with the<br />
language we got. I&#39;m figuring out whether a better morphophonology could have met the<br />
requirements. It should be much simpler.” (la bremenli)<br />
** FAQ’s for all sorts of aspects of the language and its use in practice, and for the community<br />
** Translation tips<br />
*** Record observations like “I found that this complex idea in English could be translated to<br />
this simple Lojban idea”.<br />
** Translation help center?<br />
*** Either ask for real-time help, or look through responses to already-asked questions.<br />
** List of short problems that have arisen in translation projects and their solutions<br />
** List of open projects, ideas, or questions.<br />
* Advertising is hard but retention is harder. How do we fix both?<br />
** Smooth the learning curve.<br />
** Better organize the website.<br />
** Give people projects.<br />
** Formal mentor-mentee relationships<br />
*** Suzil proposes that new learners get paired together.<br />
*** Could go with triads of one experienced language user and two newcomers.<br />
*** Keep a list of people who are currently learning/skilled, with their skill level.<br />
*** Ask for interests, skill level, native and functional secondary languages,<br />
timezone/location, goals, free times in schedule<br />
** Check-ups<br />
** Community get-togethers.<br />
<br />
** Express learning material in multiple ways. Some people are comfortable with the IPA but get<br />
confused by approximate pronunciation descriptions based on English – and IPA is easier to<br />
reference at a glance.<br />
** Voice chat rooms, some of which are not solely in Lojban.<br />
*** TeamSpeak, Mumble, etc.<br />
** Low-investment ways to encourage new speakers to join and stay.<br />
** Build community habits: certain people schedule regular times to do certain things and are kept to<br />
it. (Shame is helpful - make people rely on them)<br />
** Surveys for suggestions<br />
** Crash Course<br />
* Maintain a census of the Lojban community for data purposes and in order to keep track of who is good for<br />
what purposes.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=lo_jboce%27u_selzukseltcuste_pe_la_2017_gregOriiys_nanca&diff=122754lo jboce'u selzukseltcuste pe la 2017 gregOriiys nanca2018-04-17T20:09:05Z<p>Krtisfranks: Created page with "Desires: * Lojban community that does “lots of translations and projects and such”. * Develop a more active, less random arrangement of independent endeavors. * Need a pla..."</p>
<hr />
<div>Desires:<br />
* Lojban community that does “lots of translations and projects and such”.<br />
* Develop a more active, less random arrangement of independent endeavors.<br />
* Need a place/way to inform others of such projects. Outreach is presently problematic.<br />
* Organize the main website better. Separate out official stuff from unofficial stuff. Possibly put things into<br />
each user’s personal space if it is unofficial.<br />
* Reduce learning curve for joining community<br />
* Build a tighter, more organized, more self-aware community<br />
* Develop goals for language exploration/projects.<br />
* Retain people<br />
* Sponsor certain works so that others may see them. Keep the styles, formats, difficulties, and lengths<br />
diverse. Experiencing other people’s works will encourage people to stay with it and to contribute<br />
themselves; having one’s work appreciated will encourage one to produce more and to stay involved.<br />
<br />
Methods:<br />
* Community round-up ( https://solpahi.wordpress.com/2017/01/30/monthly-lojban- community-roundup-<br />
january-2017/ )<br />
** Advertise it. Endorse it?<br />
* Place where people can volunteer in others’ projects.<br />
** Byline/motivational quote: “Most projects could be completed within a few days or weeks if every<br />
Lojbanist wrote one line of Lojban/English every day.”<br />
* Possibly institute a monetary reward for vetted contributions of significance and merit (but allow them to<br />
be small in order to encourage participation).<br />
** Could give a reward to a randomly selected contributor each unit of time. (How would each<br />
contributor’s probability of being selected be determined?)<br />
** Or set up a bounty system: Have a board which specifies a goal/request, the conditions under<br />
which it would be met, and the reward. First person to succeed claims the bounty and it gets<br />
closed and archived.<br />
** Set up an auction. People bid on getting help or contributions/promises vie for reward.<br />
** Possible tasks: contributing translations, learning material/courses/video lectures, updating old<br />
material, cataloguing development or ideas, designing new interfaces/websites, holding<br />
community meet-ups or events, holding advertisement conferences to bring people in, flashcards,<br />
translating common interfaces (programs on phones, etc.), stories, poems, diary entries, captions<br />
for movies or television shows.<br />
** The condition would be that all work submitted would be with the CC0 content licence or similar.<br />
** Negatives:<br />
*** No contract. Could be problematic (legally or just socially – social harm could really<br />
wound our community)<br />
*** How does one determine what is fair? How do we measure work? Poor workers/work<br />
could be rewarded as much as good workers/work. Do we want to encourage<br />
participation and improvement, or do we want to generate good products?<br />
*** Requires large monetary resources.<br />
*** If money disappears, then so too will the interest.<br />
*** Possibly irrevocably alters the character of our community. Is it a community that loves a<br />
great language and wants it to succeed, or is it a business with workers who just want to<br />
make money and do not care about the product or what it means (the wider language) –<br />
and who do as little as possible while still earning it? Is this a translation factory in which<br />
every employee competes against everyone else, or a collaborative exploration of a<br />
common interest?<br />
*** Periodic Nobel-Prize-style, fixed-amount rewards from LLG coffers. Various categories;<br />
review committee; notable/best contributions rewarded.<br />
* Website ideas (a lot of this is from la .timoteios. and la .uakci):<br />
** The website should host only the official or endorsed parts and projects of Lojban.<br />
** Organize projects centrally via a web-based project-management tool.<br />
*** Perhaps: Phabricator (already used for a Lojban Speech Recognition Tool)<br />
*** Set up http://projects.lojban.org with it.<br />
*** Can also review content. Keeps things organized, centralized, official, and of<br />
quality.<br />
*** Useful for proofreading and providing direct feedback with each item.<br />
*** Can be integrated with Git and shared on GitHub. Can host CLL project.<br />
** Lojban’s web presence is confusing. What is official? What is archived? What is redundant? What<br />
is deprecated or obsolete? How can one find material about X / What is supposed to be read? How<br />
does one find advice about common topics?<br />
*** Disorganization may be due to the main website being a wiki. Anyone can add anything<br />
and it gets haphazard because no-one is designated to oversee everything.<br />
External/personal websites or alternatives, as well as forums, leave a sprawling mess.<br />
** Maintain a single, central, organized website in which everything is official and code-reviewed<br />
and reviewed by an official committee.<br />
** Make sure that all official material is translated into every main language and that any change in<br />
any of them is propagated/updated in every other version so that everything is maintained together<br />
with only one version of anything (expressed in multiple languages).<br />
** Move the current website to a new website ( wiki.lojban.org ) and link to it from the new main<br />
website with the warning that none of its content should be taken as official unless it is designated<br />
as such on the new main website.<br />
** Would need explicitly defined design goals for the website.<br />
*** Should advertise Lojban effective<br />
*** Provide accessible, up-to- date resources for Lojban (learning, usage, etc.) in all target<br />
languages.<br />
*** Clarify exactly what is official and the status/type of unofficial things.<br />
*** Function as a centralized nexus for the community.<br />
*** Invite involvement from community.<br />
*** Connect Lojbanists.<br />
*** Incorporate/mention all external Lojbanic websites, groups, blogs, etc.<br />
*** Facilitate community projects (and the reward system).<br />
*** Low cognitive barrier-to- entry<br />
*** Work well on desktop and mobile devices.<br />
*** Publish new content only upon the approval of certain people and other conditions.<br />
** Use a system which enables or automates protocols and workflows. Use software with a strict<br />
workflow.<br />
*** Wiki fails here.<br />
** Vocaroo for short audio recordings<br />
** Using the Jekyll static website generator with a plugin to support multiple languages:<br />
*** https://jekyllrb.com/<br />
*** https://github.com/Anthony-Gaudino/jekyll- multiple-languages- plugin<br />
** .PO files being a popular, open-source format for translations<br />
** Could be a plain HTML site which constantly synchronizes with a GitHub repository which in<br />
turn is connected to a workflow organization utility.<br />
*** HTML may alienate non-web- developers. Perhaps use Markdown instead? Would<br />
separate the text from the website structure – allows for manageability and translation<br />
ease.<br />
*** Suggestion for workflow organization utility: Phabricator.<br />
**** No need for GitHub accounts.<br />
**** GitHub has a high learning curve. Phabricator may be more intuitive – need to<br />
trial it.<br />
**** Phabricator is open source. Could customize it. (Translate it to Lojban?)<br />
**** Can automate rebuilding of the static site when changes/new content is<br />
introduced.<br />
**** Might be able to automate the deployment of many Lojban projects (CLL?).<br />
* Expand our community demographically in order to ensure that everything is translated and actively<br />
maintained in as many languages as possible in a translinguistically compatible way.<br />
* Find support for hosting costs.<br />
* List of some projects:<br />
** Tweet things in Lojban (including haikus)<br />
** Write poems.<br />
*** Weekly poems (pemkarni) – an ongoing effort<br />
** Answer Quora questions<br />
** Develop the Interactive Story (lo lisri pe la .norman.)<br />
** Catalogue open questions/problems/topics of exploration<br />
** Lojban Stack Exchange<br />
** Create YouTube vocab-builder slideshows.<br />
** Translate short works. (Perhaps focus on children’s literature or historically important missives).<br />
** Audio record Lojban speech in order to practice and so that others may test recognition.\<br />
** Translate important texts (Bible, etc.)<br />
** Word database<br />
*** Improve/new Anki flashcard decks<br />
*** Organize example sentences for words in one location (per word) with really good<br />
glosses and other notes.<br />
*** Organize lists of lujvo by veljvo.<br />
*** Organize gismu according to frame or the types and case roles of the sumti places.<br />
*** Organize words by frequency.<br />
*** Organize words by topic or meaning (thesaurus).<br />
** Fix sutysisku so that it works offline and does not lose its cache in Firefox.<br />
** Allow for manipulation of dictionaries and texts.<br />
*** Example: First use of a word in a text will have a gloss pop up.<br />
** Maintain list of all words of a certain type without definitions (all gismu-form words, official<br />
gismu, experimental gismu, gismu of form CCVCV, rafsi of form CVV, etc.). This will allow<br />
people to be able to easily access wordlists for programs.<br />
** Maintain a list of rafsi and their associated gismu (and example lujvo?)<br />
** “Designing rules for using terminators that require no software support to apply and that are<br />
learnable, grammatically correct, and reasonably terse. Ku will be scarce, beho more frequent.”<br />
** Figuring out how to write math with mostly bridi and few mekso, based on Robin&#39;s helpful article.<br />
** “Sketching what the language specifications and requirements must have been to come up with the<br />
language we got. I&#39;m figuring out whether a better morphophonology could have met the<br />
requirements. It should be much simpler.” (la bremenli)<br />
** FAQ’s for all sorts of aspects of the language and its use in practice, and for the community<br />
** Translation tips<br />
*** Record observations like “I found that this complex idea in English could be translated to<br />
this simple Lojban idea”.<br />
** Translation help center?<br />
*** Either ask for real-time help, or look through responses to already-asked questions.<br />
** List of short problems that have arisen in translation projects and their solutions<br />
** List of open projects, ideas, or questions.<br />
* Advertising is hard but retention is harder. How do we fix both?<br />
** Smooth the learning curve.<br />
** Better organize the website.<br />
** Give people projects.<br />
** Formal mentor-mentee relationships<br />
*** Suzil proposes that new learners get paired together.<br />
*** Could go with triads of one experienced language user and two newcomers.<br />
*** Keep a list of people who are currently learning/skilled, with their skill level.<br />
*** Ask for interests, skill level, native and functional secondary languages,<br />
timezone/location, goals, free times in schedule<br />
** Check-ups<br />
** Community get-togethers.<br />
<br />
** Express learning material in multiple ways. Some people are comfortable with the IPA but get<br />
confused by approximate pronunciation descriptions based on English – and IPA is easier to<br />
reference at a glance.<br />
** Voice chat rooms, some of which are not solely in Lojban.<br />
*** TeamSpeak, Mumble, etc.<br />
** Low-investment ways to encourage new speakers to join and stay.<br />
** Build community habits: certain people schedule regular times to do certain things and are kept to<br />
it. (Shame is helpful - make people rely on them)<br />
** Surveys for suggestions<br />
** Crash Course<br />
* Maintain a census of the Lojban community for data purposes and in order to keep track of who is good for<br />
what purposes.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Digit_Strings_which_Represent_Continued_Fractions&diff=122694Proposal: Digit Strings which Represent Continued Fractions2018-03-16T22:15:12Z<p>Krtisfranks: </p>
<hr />
<div>{{jbocre/en}}<br />
<br />
This article is a proposed description of a means by which to express numbers in a generalized continued fraction format as represented by a string of digits. It will not discuss other notations for continued fractions. By way of analogy, the subject matter of this article would be similar to a description of the decimal system (base) and will not touch on subject matter which is similar to means of expressing numbers as summations (big operator "<math>\sum</math>") or formal polynomials in <math>10</math> with coefficients in <math>\mathbb{Z} \cap [0,9]</math>, even though all of these are mutually equivalent.<br />
<br />
For the purposes of this article: All expressions are big-endian and microdigits are in traditional decimal. PEMDAS is obeyed.<br />
<br />
== Mode Activation ==<br />
<br />
== Original Explanation ==<br />
<br />
Let <math>z = a_0 + b_0/(a_1 + b_1/(a_2 + b_2/(\dots))) = a_0 + \underset{i=0}{\overset{\infty}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>a_i</math> and <math>b_i</math> are integers for all <math>i</math> (see [https://oeis.org/wiki/Continued_fractions#Gauss.27_Kettenbruch_notation Kettenbruch notation here]). In fact, for all i, we will canonically restrict <math>a_{(i+1)}</math> and <math>b_i</math> to nonnegative integers such that if <math>b_j = 0</math>, then <math>a_k = 1</math> and <math>b_k = 0</math> for all <math>k \geq j</math>; this is a perfectly natural and standard set of restrictions to make and does not actually diminish the set of numbers which are expressible in this format, but the restriction is not technically necessary for Lojban. Then we will denote <math>z</math> by the continued fraction representation <math>z = (a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math>; the whole rhs representation is called a string. Notice that the integer part is included. In this format, for each <math>i</math>, "<math>a_i : b_i</math>" forms a single unit called a macrodigit; for each <math>i</math>, "<math>a_i</math>" and "<math>b_i</math>" each are microdigits; the colon ("<math>:</math>") separates microdigits and the comma ("<math>,</math>") separates macrodigits. Microdigits can be expressed in any base or other representation and macrodigits could be reversed or slightly rearranged (such as being of form "<math>b_i : a_{(i+1)}</math>"; however, for our purposes here microdigits will be expressed in big-endian traditional decimal and macrodigits will be formed and ordered as shown; the specification herein proposed will obligate the user to express the macrodigits in the form which is shown (id est: of form "<math>a_i : b_i</math>"; within any given macrodigit, the first microdigit expressed represents <math>a_i</math> and the second (and final) microdigit expressed represents <math>b_i</math>, only) but the other features aforementioned are not guaranteed, although they may normally be assumed as a contextless default. In order to be clear: in this representation, each macrodigit will consist of exactly two microdigits - namely, <math>a_i</math> and <math>b_i</math> in that order, for all <math>i</math> - and these microdigits will be separated explicitly by "pi'e"; meanwhile, macrodigits will be separated explicitly by "pi". In this representation, I will denote a not-explicitly-specified microdigit by a pair of consecutive underscores ("<math>\_\_</math>"). In the 'big-endian' arrangement of the macrodigits (as herein depicted), the first microdigit (<math>a_0</math>) represents the 'integer part' of the expression.<br />
<br />
In this system, let "pi'e" represent ":" and let "pi" represent ",", each bijectively. Then the basic method of expressing a continued fraction is to just read <math>(a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math> where each microdigit is expressed in some base which represents integers, the parenthesis are not mentioned, the separators being named/pronounced as before, "ra'e" being used in order to create cyclic patterns or to extend the string indefinitely, and the string being terminated as any numeral string could or would be. The interpretation of the whole string according to these rules for continued fractions would be specified via JUhAU.<br />
<br />
A string terminates if and only if "ra'e" is not explicitly used. "ra'e" will couple with exactly one microdigit, and exactly every following explicitly mentioned microdigit in that position of their macrodigits will be considered to be part of a repetitious sequence applying to/running over the microdigits in that position of their macrodigits; the other microdigit is unaffected by it. Moreover, it can couple with "pi'e" as well (see below), but this occurs iff "ra'e" is explicitly mentioned immediately prior to exactly an explicitly mentioned "pi'e". If it couples with <math>a_j</math> for some <math>j</math>, then it will cyclically repeat that <math>a_j</math> and all explicitly mentioned <math>a_{(j+k)}</math> for all <math>k>0</math> in each <math>a_i</math> spot until the last <math>b_i</math> (which either will be explicitly mentioned and defined as last by the closure of the string scope (formally, all subsequent <math>b_i</math> will be trivial), or will be nonexistent according to the next point); iff it couples with <math>b_j</math> for some <math>j</math>, then the string is extended to infinite length and there exists no 'last <math>b_i</math>' (meaning that any repetition on <math>a_i</math> will also continue ad infinitum).<br />
Thus, <math>(a_0:b_0, a_1:b_1, \operatorname{ra'e} a_2:b_2, a_3:b_3, \_\_:b_4, \_\_:b_5, \_\_:b_6, \dots, \_\_:b_{10}, \_\_:\operatorname{ra'e} b_{11}) = (a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, a_2:b_4, a_3:b_5, a_2:b_6, a_3:b_7, a_2:b_8, a_3:b_9, a_2:b_{10}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, \dots)</math>.<br />
<br />
Additional rules:<br />
* For any <math>i>0</math>, if <math>a_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math>. <math>a_0 = 0</math> if it is not explicitly mentioned unless context very clearly indicates otherwise. These are called "context-dependent defaults".<br />
* For any <math>i</math>, if <math>b_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math> if the string continues (explicitly or by sufficient "ra'e") and <math>0</math> otherwise. This is especially true if the verbal expression of the string is terminated and "ra'e" was not explicitly used (on <math>b_j</math> for some <math>j</math>): all finite strings can infinitely extended by right-concatenating "<math>1:0, 1:0, 1:0, \dots)</math> to them (this is similar to decimal notation; for example: <math>8.23 = 8.23000\dots</math>). These are called "context-dependent defaults".<br />
* If exactly one microdigit is explicitly mentioned in a given macrodigit, then: it is to be understood to be <math>a_i</math> iff "ra'e" did not couple with "pi'e"; regardless of the prior presence of "ra'e pi'e" in the string, the implicit microdigit will assume the generic default value or (preferably) the value according to a repetition or formula which it inherited (see the aforementioned context-dependent defaults).<br />
<br />
Even though the basic and assumed notation for <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> is <math>(a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, \dots)</math> (this is so-called 'big-endian' in the macrodigits), other formats can be supported iff they are explicitly specified. For example, with a change of endianness in the macrodigits, <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, a_3:b_3, a_2:b_2, a_1:b_1, a_0:b_0)</math>. It is also reasonable that the microdigits could be reordered (note that this is not a change in the endianness of each microdigit (which would change <math>12:34</math> to <math>21:43</math>); rather, it is a transposition of the microdigits within each macrodigit) like so: <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, b_3:a_3, b_2:a_2, b_1:a_1, b_0:a_0)</math>; notice that in this example, I also changed the endianness of the macrodigits because the expression does not make much intuitive sense otherwise (but it would nonetheless be possible to do merely one of these changes in isolation, even if it is not advisable or sensical).<br />
<br />
The string will terminate and be interpreted as a number formed from the specified continued fraction as all other digits strings do (see my other work).<br />
<br />
-- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 08:10, 9 March 2018 (UTC)<br />
<br />
== Alternative Explanation ==<br />
<br />
The description in this section is intended to provide the same results as those in the "Original Explanation" section.<br />
<br />
Zeroth, the mode must be activated (as described previously).<br />
<br />
Throughout the following discussions, I shall assume that such mode activation has been performed as appropriate.<br />
<br />
For some <math>n \in \mathbb{N} \cup \{0, +\infty\}</math> and some sequences <math>(a_i)_i, (b_i)_i</math>, we will map <math>z = a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> (math form) to a string of form <math>(a_0:b_0, a_1:b_1, a_2:b_2, \dots, a_n:b_n)</math> (this is the notational form), which would be pronounced more or less as "a<sub>0</sub> pi'e b<sub>0</sub> pi a<sub>1</sub> pi'e b<sub>1</sub> pi a<sub>2</sub> pi'e b<sub>2</sub> pi ... a<sub>n</sub> pi'e b<sub>n</sub>" (this is the verbal form). In other words, each "''':'''" in the notational form is expressed as "pi'e" and each "''','''" in the notational form is expressed as "pi", and vice-versa, where "pi'e" and "pi" are exactly the cmavo that you think that they are. Notice that the parenthesis in the notation form are not pronounced; they are used in the notational form so that readers understand that everything between them forms some sort of unit - however, in Lojban, the terms are read and first understood as digits which compile into some sort of numeric string, so this is not necessary; moreover, mode activation makes it clear that they are indeed a single unit (and what that unit means: namely, a continued fraction).<br />
<br />
(<u>'''Technical aside'''</u>: In the original math form, each '''a<sub>i</sub>''' and '''b<sub>i</sub>''' are terms in their respective sequences and can be more or less understood as indirect terms in the continued fraction (really, the ordered pairs are the operands of the '''K''' operator and the entries of the pairs are the terms of the sequences); we are performing an implicit sleight of hand in mapping these numbers to digits in the string form, and we notate them exactly the same. This latter fact can be seen if one realizes the "pi'e" and "pi" are themselves digits and can only be concatenated to other digits. So, I may end up using the words "term" and "digit" more or less interchangeably (making the assumption that the reader knows when I am not including "pi'e" and "pi" in my reference set); they are technically distinct in concept and domain, but they are isomorphic. For the record, each 'term' in string notation may actually be constituted by more than one 'digit' in the expansion; for example, '''a<sub>0</sub> = 3*4''' would mean that the expression "a<sub>0</sub>" in the string would have to be represented by the multidigit expression "12" in decimal notation. Technically, I would call "a<sub>i</sub>" and "a<sub>b</sub>" macrodigits (and "12", standing in for such a macrodigit, is itself a macrodigit) and these can be composed of microdigits (which, in the example, would be "1" and "2" in that order). I will assume that microdigits are to be interpreted in decimal form (so a "1" followed by a "2", and nothing else being involved, compiles to "12" and means the number twelve) throughout this page; this assumption can be changed by certain cmavo if so desired.)<br />
<br />
Now, it might be nice to avoid having to talk forever in the case of <math>n = +\infty</math> or to not have to say or repeat digits that follow a pattern. The following sections address these concerns. However, we first must cover the simplest cases - at the very least because they serve as good entry-level examples.<br />
<br />
=== Step 1: Simplest (and Finite) Case ===<br />
<br />
Let <math>n \in \mathbb{N} \cup \{0\}</math>. Consider the continued fraction <math>z = a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>\forall i, a_i</math> & <math>b_i</math> will be explicitly defined, particularly as they arise. We can enforce conditions on the sequences <math>(a_i)_i</math> & <math>(b_i)_i</math>, but we will ignore such details, because we just need formal continued fractions. Since '''n''' is finite, we will not use the word "ra'e" on any of the '''b<sub>i</sub>''' terms in this case/section.<br />
<br />
We can transform the representation of <math>z</math> from the previous notation (which is the application of a mathematical operator) to a string of digits. This is similar to changing "'''2*5'''" to "10".<br />
<br />
The simplest subcase is if <math>b_i = 0 \forall i</math>. In that subcase, '''z = a<sub>0</sub>'''. In string form, '''z''' would be written as "(a<sub>0</sub>:0, 0:0, 0:0, ...)", which collapses to "(a<sub>0</sub>)". Since we are assuming that '''n''' is finite and that we are explicitly stating the value of any nontrivial term ('''a<sub>i</sub>''' and '''b<sub>i</sub>'''), we take the sequence to 'terminate' with the last explicitly mentioned term (and all subsequent terms to be trivial - which is to say that they need not be mentioned). In particular, if the last explicitly mentioned term is '''a<sub>i</sub>''', then '''b<sub>i</sub> = 0'''; if the last explicitly mentioned term is '''b<sub>i</sub>''', then '''a<sub>(i+1)</sub> = 1''' and '''b<sub>(i+1)</sub> = 0'''; these particular values are 'trivial'. It does not matter what the later terms in the sequences are due to the nature of fractions (so long as we do not divide by zero - which we shall assume). Note that explicitly mentioned terms need not be ''non''trivial; however, if the last explicitly mentioned term was trivial, then the expression could have been simplified by having not explicitly mentioned it either. In the string representation, only the explicitly mentioned terms need be shown/said (and simplifications such as the one just stated are always welcome); in other words, we do not need to say any later '''a<sub>i</sub>''' or '''b<sub>i</sub>''' or - indeed - even the "pi" ("''','''") immediately after the last explicitly mentioned term. We also introduce the rule - used throughout this page - that (unless a certain condition is satisfied, which shall be addressed later), if exactly one macrodigit is explicitly mentioned between "pi"s, then it represents '''a<sub>i</sub>''' (for appropriate '''i'''). Thus "(a<sub>0</sub>)" is pronounced simply as "a<sub>0</sub>", whatever that is. In that situation, the '''b<sub>i</sub>''' with which it is paired will take the default value - in this example, 0. For example, the extremely trivial continued fraction '''12''' (twelve), which equals <math>12 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{0}{a_{i+1}}\big)</math> for any sequence <math>(a_i)_i: a_0 = 12 \& a_i \neq 0\forall i</math>, is pronounced simply as "pa re" (assuming that continued fraction interpretation has been activated and microdigits are expressed in decimal notation).</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Digit_Strings_which_Represent_Continued_Fractions&diff=122693Proposal: Digit Strings which Represent Continued Fractions2018-03-16T21:47:42Z<p>Krtisfranks: /* Step 1: Simplest (and Finite) Case */</p>
<hr />
<div>{{jbocre/en}}<br />
<br />
This article is a proposed description of a means by which to express numbers in a generalized continued fraction format as represented by a string of digits. It will not discuss other notations for continued fractions. By way of analogy, the subject matter of this article would be similar to a description of the decimal system (base) and will not touch on subject matter which is similar to means of expressing numbers as summations (big operator "<math>\sum</math>") or formal polynomials in <math>10</math> with coefficients in <math>\mathbb{Z} \cap [0,9]</math>, even though all of these are mutually equivalent.<br />
<br />
For the purposes of this article: All expressions are big-endian and microdigits are in traditional decimal. PEMDAS is obeyed.<br />
<br />
== Mode Activation ==<br />
<br />
== Original Explanation ==<br />
<br />
Let <math>z = a_0 + b_0/(a_1 + b_1/(a_2 + b_2/(\dots))) = a_0 + \underset{i=0}{\overset{\infty}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>a_i</math> and <math>b_i</math> are integers for all <math>i</math> (see [https://oeis.org/wiki/Continued_fractions#Gauss.27_Kettenbruch_notation Kettenbruch notation here]). In fact, for all i, we will canonically restrict <math>a_{(i+1)}</math> and <math>b_i</math> to nonnegative integers such that if <math>b_j = 0</math>, then <math>a_k = 1</math> and <math>b_k = 0</math> for all <math>k \geq j</math>; this is a perfectly natural and standard set of restrictions to make and does not actually diminish the set of numbers which are expressible in this format, but the restriction is not technically necessary for Lojban. Then we will denote <math>z</math> by the continued fraction representation <math>z = (a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math>; the whole rhs representation is called a string. Notice that the integer part is included. In this format, for each <math>i</math>, "<math>a_i : b_i</math>" forms a single unit called a macrodigit; for each <math>i</math>, "<math>a_i</math>" and "<math>b_i</math>" each are microdigits; the colon ("<math>:</math>") separates microdigits and the comma ("<math>,</math>") separates macrodigits. Microdigits can be expressed in any base or other representation and macrodigits could be reversed or slightly rearranged (such as being of form "<math>b_i : a_{(i+1)}</math>"; however, for our purposes here microdigits will be expressed in big-endian traditional decimal and macrodigits will be formed and ordered as shown; the specification herein proposed will obligate the user to express the macrodigits in the form which is shown (id est: of form "<math>a_i : b_i</math>"; within any given macrodigit, the first microdigit expressed represents <math>a_i</math> and the second (and final) microdigit expressed represents <math>b_i</math>, only) but the other features aforementioned are not guaranteed, although they may normally be assumed as a contextless default. In order to be clear: in this representation, each macrodigit will consist of exactly two microdigits - namely, <math>a_i</math> and <math>b_i</math> in that order, for all <math>i</math> - and these microdigits will be separated explicitly by "pi'e"; meanwhile, macrodigits will be separated explicitly by "pi". In this representation, I will denote a not-explicitly-specified microdigit by a pair of consecutive underscores ("<math>\_\_</math>"). In the 'big-endian' arrangement of the macrodigits (as herein depicted), the first microdigit (<math>a_0</math>) represents the 'integer part' of the expression.<br />
<br />
In this system, let "pi'e" represent ":" and let "pi" represent ",", each bijectively. Then the basic method of expressing a continued fraction is to just read <math>(a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math> where each microdigit is expressed in some base which represents integers, the parenthesis are not mentioned, the separators being named/pronounced as before, "ra'e" being used in order to create cyclic patterns or to extend the string indefinitely, and the string being terminated as any numeral string could or would be. The interpretation of the whole string according to these rules for continued fractions would be specified via JUhAU.<br />
<br />
A string terminates if and only if "ra'e" is not explicitly used. "ra'e" will couple with exactly one microdigit, and exactly every following explicitly mentioned microdigit in that position of their macrodigits will be considered to be part of a repetitious sequence applying to/running over the microdigits in that position of their macrodigits; the other microdigit is unaffected by it. Moreover, it can couple with "pi'e" as well (see below), but this occurs iff "ra'e" is explicitly mentioned immediately prior to exactly an explicitly mentioned "pi'e". If it couples with <math>a_j</math> for some <math>j</math>, then it will cyclically repeat that <math>a_j</math> and all explicitly mentioned <math>a_{(j+k)}</math> for all <math>k>0</math> in each <math>a_i</math> spot until the last <math>b_i</math> (which either will be explicitly mentioned and defined as last by the closure of the string scope (formally, all subsequent <math>b_i</math> will be trivial), or will be nonexistent according to the next point); iff it couples with <math>b_j</math> for some <math>j</math>, then the string is extended to infinite length and there exists no 'last <math>b_i</math>' (meaning that any repetition on <math>a_i</math> will also continue ad infinitum).<br />
Thus, <math>(a_0:b_0, a_1:b_1, \operatorname{ra'e} a_2:b_2, a_3:b_3, \_\_:b_4, \_\_:b_5, \_\_:b_6, \dots, \_\_:b_{10}, \_\_:\operatorname{ra'e} b_{11}) = (a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, a_2:b_4, a_3:b_5, a_2:b_6, a_3:b_7, a_2:b_8, a_3:b_9, a_2:b_{10}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, \dots)</math>.<br />
<br />
Additional rules:<br />
* For any <math>i>0</math>, if <math>a_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math>. These are called "context-dependent defaults". <math>a_0 = 0</math> if it is not explicitly mentioned unless context very clearly indicates otherwise.<br />
* For any <math>i</math>, if <math>b_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math> if the string continues (explicitly or by sufficient "ra'e") and <math>0</math> otherwise. This is especially true if the verbal expression of the string is terminated and "ra'e" was not explicitly used (on <math>b_j</math> for some <math>j</math>): all finite strings can infinitely extended by right-concatenating "<math>1:0, 1:0, 1:0, \dots)</math> to them (this is similar to decimal notation; for example: <math>8.23 = 8.23000\dots</math>). These are called "context-dependent defaults".<br />
* If exactly one microdigit is explicitly mentioned in a given macrodigit, then: it is to be understood to be <math>a_i</math> iff "ra'e" did not couple with "pi'e"; regardless of the prior presence of "ra'e pi'e" in the string, the implicit microdigit will assume the generic default value or (preferably) the value according to a repetition or formula which it inherited (see the aforementioned context-dependent defaults).<br />
<br />
Even though the basic and assumed notation for <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> is <math>(a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, \dots)</math> (this is so-called 'big-endian' in the macrodigits), other formats can be supported iff they are explicitly specified. For example, with a change of endianness in the macrodigits, <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, a_3:b_3, a_2:b_2, a_1:b_1, a_0:b_0)</math>. It is also reasonable that the microdigits could be reordered (note that this is not a change in the endianness of each microdigit (which would change <math>12:34</math> to <math>21:43</math>); rather, it is a transposition of the microdigits within each macrodigit) like so: <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, b_3:a_3, b_2:a_2, b_1:a_1, b_0:a_0)</math>; notice that in this example, I also changed the endianness of the macrodigits because the expression does not make much intuitive sense otherwise (but it would nonetheless be possible to do merely one of these changes in isolation, even if it is not advisable or sensical).<br />
<br />
The string will terminate and be interpreted as a number formed from the specified continued fraction as all other digits strings do (see my other work).<br />
<br />
-- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 08:10, 9 March 2018 (UTC)<br />
<br />
== Alternative Explanation ==<br />
<br />
The description in this section is intended to provide the same results as those in the "Original Explanation" section.<br />
<br />
Zeroth, the mode must be activated (as described previously).<br />
<br />
Throughout the following discussions, I shall assume that such mode activation has been performed as appropriate.<br />
<br />
For some <math>n \in \mathbb{N} \cup \{0, +\infty\}</math> and some sequences <math>(a_i)_i, (b_i)_i</math>, we will map <math>z = a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> (math form) to a string of form <math>(a_0:b_0, a_1:b_1, a_2:b_2, \dots, a_n:b_n)</math> (this is the notational form), which would be pronounced more or less as "a<sub>0</sub> pi'e b<sub>0</sub> pi a<sub>1</sub> pi'e b<sub>1</sub> pi a<sub>2</sub> pi'e b<sub>2</sub> pi ... a<sub>n</sub> pi'e b<sub>n</sub>" (this is the verbal form). In other words, each "''':'''" in the notational form is expressed as "pi'e" and each "''','''" in the notational form is expressed as "pi", and vice-versa, where "pi'e" and "pi" are exactly the cmavo that you think that they are. Notice that the parenthesis in the notation form are not pronounced; they are used in the notational form so that readers understand that everything between them forms some sort of unit - however, in Lojban, the terms are read and first understood as digits which compile into some sort of numeric string, so this is not necessary; moreover, mode activation makes it clear that they are indeed a single unit (and what that unit means: namely, a continued fraction).<br />
<br />
(<u>'''Technical aside'''</u>: In the original math form, each '''a<sub>i</sub>''' and '''b<sub>i</sub>''' are terms in their respective sequences and can be more or less understood as indirect terms in the continued fraction (really, the ordered pairs are the operands of the '''K''' operator and the entries of the pairs are the terms of the sequences); we are performing an implicit sleight of hand in mapping these numbers to digits in the string form, and we notate them exactly the same. This latter fact can be seen if one realizes the "pi'e" and "pi" are themselves digits and can only be concatenated to other digits. So, I may end up using the words "term" and "digit" more or less interchangeably (making the assumption that the reader knows when I am not including "pi'e" and "pi" in my reference set); they are technically distinct in concept and domain, but they are isomorphic. For the record, each 'term' in string notation may actually be constituted by more than one 'digit' in the expansion; for example, '''a<sub>0</sub> = 3*4''' would mean that the expression "a<sub>0</sub>" in the string would have to be represented by the multidigit expression "12" in decimal notation. Technically, I would call "a<sub>i</sub>" and "a<sub>b</sub>" macrodigits (and "12", standing in for such a macrodigit, is itself a macrodigit) and these can be composed of microdigits (which, in the example, would be "1" and "2" in that order). I will assume that microdigits are to be interpreted in decimal form (so a "1" followed by a "2", and nothing else being involved, compiles to "12" and means the number twelve) throughout this page; this assumption can be changed by certain cmavo if so desired.)<br />
<br />
Now, it might be nice to avoid having to talk forever in the case of <math>n = +\infty</math> or to not have to say or repeat digits that follow a pattern. The following sections address these concerns. However, we first must cover the simplest cases - at the very least because they serve as good entry-level examples.<br />
<br />
=== Step 1: Simplest (and Finite) Case ===<br />
<br />
Let <math>n \in \mathbb{N} \cup \{0\}</math>. Consider the continued fraction <math>z = a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>\forall i, a_i</math> & <math>b_i</math> will be explicitly defined, particularly as they arise. We can enforce conditions on the sequences <math>(a_i)_i</math> & <math>(b_i)_i</math>, but we will ignore such details, because we just need formal continued fractions. Since '''n''' is finite, we will not use the word "ra'e" on any of the '''b<sub>i</sub>''' terms in this case/section.<br />
<br />
We can transform the representation of <math>z</math> from the previous notation (which is the application of a mathematical operator) to a string of digits. This is similar to changing "'''2*5'''" to "10".<br />
<br />
The simplest subcase is if <math>b_i = 0 \forall i</math>. In that subcase, '''z = a<sub>0</sub>'''. In string form, '''z''' would be written as "(a<sub>0</sub>:0, 0:0, 0:0, ...)", which collapses to "(a<sub>0</sub>)". Since we are assuming that '''n''' is finite and that we are explicitly stating the value of any nontrivial term ('''a<sub>i</sub>''' and '''b<sub>i</sub>'''), we take the sequence to 'terminate' with the last explicitly mentioned term (and all subsequent terms to be trivial - which is to say that they need not be mentioned). In particular, if the last explicitly mentioned term is '''a<sub>i</sub>''', then '''b<sub>i</sub> = 0'''; if the last explicitly mentioned term is '''b<sub>i</sub>''', then '''a<sub>(i+1)</sub> = 1''' and '''b<sub>(i+1)</sub> = 0'''; these particular values are 'trivial'. It does not matter what the later terms in the sequences are due to the nature of fractions (so long as we do not divide by zero - which we shall assume). Note that explicitly mentioned terms need not be ''non''trivial; however, if the last explicitly mentioned term was trivial, then the expression could have been simplified by having not explicitly mentioned it either. In the string representation, only the explicitly mentioned terms need be shown/said (and simplifications such as the one just stated are always welcome); in other words, we do not need to say any later '''a<sub>i</sub>''' or '''b<sub>i</sub>''' or - indeed - even the "pi" ("''','''") immediately after the last explicitly mentioned term. We also introduce the rule - used throughout this page - that (unless a certain condition is satisfied, which shall be addressed later), if exactly one macrodigit is explicitly mentioned between "pi"s, then it represents '''a<sub>i</sub>''' (for appropriate '''i'''). Thus "(a<sub>0</sub>)" is pronounced simply as "a<sub>0</sub>", whatever that is. For example, the extremely trivial continued fraction '''12''' (twelve), which equals <math>12 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{0}{a_{i+1}}\big)</math> for any sequence <math>(a_i)_i: a_0 = 12 \& a_i \neq 0\forall i</math>, is pronounced simply as "pa re" (assuming that continued fraction interpretation has been activated and microdigits are expressed in decimal notation).</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Digit_Strings_which_Represent_Continued_Fractions&diff=122692Proposal: Digit Strings which Represent Continued Fractions2018-03-16T21:46:11Z<p>Krtisfranks: /* Step 1: Simplest (and Finite) Case */</p>
<hr />
<div>{{jbocre/en}}<br />
<br />
This article is a proposed description of a means by which to express numbers in a generalized continued fraction format as represented by a string of digits. It will not discuss other notations for continued fractions. By way of analogy, the subject matter of this article would be similar to a description of the decimal system (base) and will not touch on subject matter which is similar to means of expressing numbers as summations (big operator "<math>\sum</math>") or formal polynomials in <math>10</math> with coefficients in <math>\mathbb{Z} \cap [0,9]</math>, even though all of these are mutually equivalent.<br />
<br />
For the purposes of this article: All expressions are big-endian and microdigits are in traditional decimal. PEMDAS is obeyed.<br />
<br />
== Mode Activation ==<br />
<br />
== Original Explanation ==<br />
<br />
Let <math>z = a_0 + b_0/(a_1 + b_1/(a_2 + b_2/(\dots))) = a_0 + \underset{i=0}{\overset{\infty}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>a_i</math> and <math>b_i</math> are integers for all <math>i</math> (see [https://oeis.org/wiki/Continued_fractions#Gauss.27_Kettenbruch_notation Kettenbruch notation here]). In fact, for all i, we will canonically restrict <math>a_{(i+1)}</math> and <math>b_i</math> to nonnegative integers such that if <math>b_j = 0</math>, then <math>a_k = 1</math> and <math>b_k = 0</math> for all <math>k \geq j</math>; this is a perfectly natural and standard set of restrictions to make and does not actually diminish the set of numbers which are expressible in this format, but the restriction is not technically necessary for Lojban. Then we will denote <math>z</math> by the continued fraction representation <math>z = (a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math>; the whole rhs representation is called a string. Notice that the integer part is included. In this format, for each <math>i</math>, "<math>a_i : b_i</math>" forms a single unit called a macrodigit; for each <math>i</math>, "<math>a_i</math>" and "<math>b_i</math>" each are microdigits; the colon ("<math>:</math>") separates microdigits and the comma ("<math>,</math>") separates macrodigits. Microdigits can be expressed in any base or other representation and macrodigits could be reversed or slightly rearranged (such as being of form "<math>b_i : a_{(i+1)}</math>"; however, for our purposes here microdigits will be expressed in big-endian traditional decimal and macrodigits will be formed and ordered as shown; the specification herein proposed will obligate the user to express the macrodigits in the form which is shown (id est: of form "<math>a_i : b_i</math>"; within any given macrodigit, the first microdigit expressed represents <math>a_i</math> and the second (and final) microdigit expressed represents <math>b_i</math>, only) but the other features aforementioned are not guaranteed, although they may normally be assumed as a contextless default. In order to be clear: in this representation, each macrodigit will consist of exactly two microdigits - namely, <math>a_i</math> and <math>b_i</math> in that order, for all <math>i</math> - and these microdigits will be separated explicitly by "pi'e"; meanwhile, macrodigits will be separated explicitly by "pi". In this representation, I will denote a not-explicitly-specified microdigit by a pair of consecutive underscores ("<math>\_\_</math>"). In the 'big-endian' arrangement of the macrodigits (as herein depicted), the first microdigit (<math>a_0</math>) represents the 'integer part' of the expression.<br />
<br />
In this system, let "pi'e" represent ":" and let "pi" represent ",", each bijectively. Then the basic method of expressing a continued fraction is to just read <math>(a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math> where each microdigit is expressed in some base which represents integers, the parenthesis are not mentioned, the separators being named/pronounced as before, "ra'e" being used in order to create cyclic patterns or to extend the string indefinitely, and the string being terminated as any numeral string could or would be. The interpretation of the whole string according to these rules for continued fractions would be specified via JUhAU.<br />
<br />
A string terminates if and only if "ra'e" is not explicitly used. "ra'e" will couple with exactly one microdigit, and exactly every following explicitly mentioned microdigit in that position of their macrodigits will be considered to be part of a repetitious sequence applying to/running over the microdigits in that position of their macrodigits; the other microdigit is unaffected by it. Moreover, it can couple with "pi'e" as well (see below), but this occurs iff "ra'e" is explicitly mentioned immediately prior to exactly an explicitly mentioned "pi'e". If it couples with <math>a_j</math> for some <math>j</math>, then it will cyclically repeat that <math>a_j</math> and all explicitly mentioned <math>a_{(j+k)}</math> for all <math>k>0</math> in each <math>a_i</math> spot until the last <math>b_i</math> (which either will be explicitly mentioned and defined as last by the closure of the string scope (formally, all subsequent <math>b_i</math> will be trivial), or will be nonexistent according to the next point); iff it couples with <math>b_j</math> for some <math>j</math>, then the string is extended to infinite length and there exists no 'last <math>b_i</math>' (meaning that any repetition on <math>a_i</math> will also continue ad infinitum).<br />
Thus, <math>(a_0:b_0, a_1:b_1, \operatorname{ra'e} a_2:b_2, a_3:b_3, \_\_:b_4, \_\_:b_5, \_\_:b_6, \dots, \_\_:b_{10}, \_\_:\operatorname{ra'e} b_{11}) = (a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, a_2:b_4, a_3:b_5, a_2:b_6, a_3:b_7, a_2:b_8, a_3:b_9, a_2:b_{10}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, \dots)</math>.<br />
<br />
Additional rules:<br />
* For any <math>i>0</math>, if <math>a_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math>. These are called "context-dependent defaults". <math>a_0 = 0</math> if it is not explicitly mentioned unless context very clearly indicates otherwise.<br />
* For any <math>i</math>, if <math>b_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math> if the string continues (explicitly or by sufficient "ra'e") and <math>0</math> otherwise. This is especially true if the verbal expression of the string is terminated and "ra'e" was not explicitly used (on <math>b_j</math> for some <math>j</math>): all finite strings can infinitely extended by right-concatenating "<math>1:0, 1:0, 1:0, \dots)</math> to them (this is similar to decimal notation; for example: <math>8.23 = 8.23000\dots</math>). These are called "context-dependent defaults".<br />
* If exactly one microdigit is explicitly mentioned in a given macrodigit, then: it is to be understood to be <math>a_i</math> iff "ra'e" did not couple with "pi'e"; regardless of the prior presence of "ra'e pi'e" in the string, the implicit microdigit will assume the generic default value or (preferably) the value according to a repetition or formula which it inherited (see the aforementioned context-dependent defaults).<br />
<br />
Even though the basic and assumed notation for <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> is <math>(a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, \dots)</math> (this is so-called 'big-endian' in the macrodigits), other formats can be supported iff they are explicitly specified. For example, with a change of endianness in the macrodigits, <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, a_3:b_3, a_2:b_2, a_1:b_1, a_0:b_0)</math>. It is also reasonable that the microdigits could be reordered (note that this is not a change in the endianness of each microdigit (which would change <math>12:34</math> to <math>21:43</math>); rather, it is a transposition of the microdigits within each macrodigit) like so: <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, b_3:a_3, b_2:a_2, b_1:a_1, b_0:a_0)</math>; notice that in this example, I also changed the endianness of the macrodigits because the expression does not make much intuitive sense otherwise (but it would nonetheless be possible to do merely one of these changes in isolation, even if it is not advisable or sensical).<br />
<br />
The string will terminate and be interpreted as a number formed from the specified continued fraction as all other digits strings do (see my other work).<br />
<br />
-- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 08:10, 9 March 2018 (UTC)<br />
<br />
== Alternative Explanation ==<br />
<br />
The description in this section is intended to provide the same results as those in the "Original Explanation" section.<br />
<br />
Zeroth, the mode must be activated (as described previously).<br />
<br />
Throughout the following discussions, I shall assume that such mode activation has been performed as appropriate.<br />
<br />
For some <math>n \in \mathbb{N} \cup \{0, +\infty\}</math> and some sequences <math>(a_i)_i, (b_i)_i</math>, we will map <math>z = a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> (math form) to a string of form <math>(a_0:b_0, a_1:b_1, a_2:b_2, \dots, a_n:b_n)</math> (this is the notational form), which would be pronounced more or less as "a<sub>0</sub> pi'e b<sub>0</sub> pi a<sub>1</sub> pi'e b<sub>1</sub> pi a<sub>2</sub> pi'e b<sub>2</sub> pi ... a<sub>n</sub> pi'e b<sub>n</sub>" (this is the verbal form). In other words, each "''':'''" in the notational form is expressed as "pi'e" and each "''','''" in the notational form is expressed as "pi", and vice-versa, where "pi'e" and "pi" are exactly the cmavo that you think that they are. Notice that the parenthesis in the notation form are not pronounced; they are used in the notational form so that readers understand that everything between them forms some sort of unit - however, in Lojban, the terms are read and first understood as digits which compile into some sort of numeric string, so this is not necessary; moreover, mode activation makes it clear that they are indeed a single unit (and what that unit means: namely, a continued fraction).<br />
<br />
(<u>'''Technical aside'''</u>: In the original math form, each '''a<sub>i</sub>''' and '''b<sub>i</sub>''' are terms in their respective sequences and can be more or less understood as indirect terms in the continued fraction (really, the ordered pairs are the operands of the '''K''' operator and the entries of the pairs are the terms of the sequences); we are performing an implicit sleight of hand in mapping these numbers to digits in the string form, and we notate them exactly the same. This latter fact can be seen if one realizes the "pi'e" and "pi" are themselves digits and can only be concatenated to other digits. So, I may end up using the words "term" and "digit" more or less interchangeably (making the assumption that the reader knows when I am not including "pi'e" and "pi" in my reference set); they are technically distinct in concept and domain, but they are isomorphic. For the record, each 'term' in string notation may actually be constituted by more than one 'digit' in the expansion; for example, '''a<sub>0</sub> = 3*4''' would mean that the expression "a<sub>0</sub>" in the string would have to be represented by the multidigit expression "12" in decimal notation. Technically, I would call "a<sub>i</sub>" and "a<sub>b</sub>" macrodigits (and "12", standing in for such a macrodigit, is itself a macrodigit) and these can be composed of microdigits (which, in the example, would be "1" and "2" in that order). I will assume that microdigits are to be interpreted in decimal form (so a "1" followed by a "2", and nothing else being involved, compiles to "12" and means the number twelve) throughout this page; this assumption can be changed by certain cmavo if so desired.)<br />
<br />
Now, it might be nice to avoid having to talk forever in the case of <math>n = +\infty</math> or to not have to say or repeat digits that follow a pattern. The following sections address these concerns. However, we first must cover the simplest cases - at the very least because they serve as good entry-level examples.<br />
<br />
=== Step 1: Simplest (and Finite) Case ===<br />
<br />
Let <math>n \in \mathbb{N} \cup \{0\}</math>. Consider the continued fraction <math>z = a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>\forall i, a_i</math> & <math>b_i</math> will be explicitly defined, particularly as they arise. We can enforce conditions on the sequences <math>(a_i)_i</math> & <math>(b_i)_i</math>, but we will ignore such details, because we just need formal continued fractions. Since '''n''' is finite, we will not use the word "ra'e" on any of the '''b<sub>i</sub>''' terms in this case/section.<br />
<br />
We can transform the representation of <math>z</math> from the previous notation (which is the application of a mathematical operator) to a string of digits. This is similar to changing "'''2*5'''" to "10".<br />
<br />
The simplest subcase is if <math>b_i = 0 \forall i</math>. In that subcase, '''z = a<sub>0</sub>'''. In string form, '''z''' would be written as "(a<sub>0</sub>:0, 0:0, 0:0, ...)", which collapses to "(a<sub>0</sub>)". Since we are assuming that '''n''' is finite and that we are explicitly stating the value of any nontrivial term ('''a<sub>i</sub>''' and '''b<sub>i</sub>'''), we take the sequence to 'terminate' with the last explicitly mentioned term (and all subsequent terms to be trivial - which is to say that they need not be mentioned). In particular, if the last explicitly mentioned term is '''a<sub>i</sub>''', then '''b<sub>i</sub> = 0'''; if the last explicitly mentioned term is '''b<sub>i</sub>''', then '''a<sub>(i+1)</sub> = 1''' and '''b<sub>(i+1)</sub> = 0'''; these particular values are 'trivial'. It does not matter what the later terms in the sequences are due to the nature of fractions (so long as we do not divide by zero - which we shall assume). Note that explicitly mentioned terms need not be ''non''trivial; however, if the last explicitly mentioned term was trivial, then the expression could have been simplified by having not explicitly mentioned it either. In the string representation, only the explicitly mentioned terms need be shown/said (and simplifications such as the one just stated are always welcome); in other words, we do not need to say any later '''a<sub>i</sub>''' or b<sub>i</sub>''' or - indeed - even the "pi" ("''','''") immediately after the last explicitly mentioned term. We also introduce the rule - used throughout this page - that (except if a certain condition is satisfied, which shall be addressed later), if exactly one macrodigit is explicitly mentioned between "pi"s, then it represents '''a<sub>i</sub>''' (for appropriate '''i'''). Thus "(a<sub>0</sub>)" is pronounced simply as "a<sub>0</sub>", whatever that is. For example, the extremely trivial continued fraction '''12''' (twelve), which equals <math>12 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{0}{a_{i+1}}\big)</math> for any sequence <math>(a_i)_i: a_0 = 12 \& a_i \neq 0\forall i</math>, is pronounced simply as "pa re" (assuming that continued fraction interpretation has been activated and microdigits are expressed in decimal notation).</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Digit_Strings_which_Represent_Continued_Fractions&diff=122691Proposal: Digit Strings which Represent Continued Fractions2018-03-16T21:45:28Z<p>Krtisfranks: /* Original Explanation */</p>
<hr />
<div>{{jbocre/en}}<br />
<br />
This article is a proposed description of a means by which to express numbers in a generalized continued fraction format as represented by a string of digits. It will not discuss other notations for continued fractions. By way of analogy, the subject matter of this article would be similar to a description of the decimal system (base) and will not touch on subject matter which is similar to means of expressing numbers as summations (big operator "<math>\sum</math>") or formal polynomials in <math>10</math> with coefficients in <math>\mathbb{Z} \cap [0,9]</math>, even though all of these are mutually equivalent.<br />
<br />
For the purposes of this article: All expressions are big-endian and microdigits are in traditional decimal. PEMDAS is obeyed.<br />
<br />
== Mode Activation ==<br />
<br />
== Original Explanation ==<br />
<br />
Let <math>z = a_0 + b_0/(a_1 + b_1/(a_2 + b_2/(\dots))) = a_0 + \underset{i=0}{\overset{\infty}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>a_i</math> and <math>b_i</math> are integers for all <math>i</math> (see [https://oeis.org/wiki/Continued_fractions#Gauss.27_Kettenbruch_notation Kettenbruch notation here]). In fact, for all i, we will canonically restrict <math>a_{(i+1)}</math> and <math>b_i</math> to nonnegative integers such that if <math>b_j = 0</math>, then <math>a_k = 1</math> and <math>b_k = 0</math> for all <math>k \geq j</math>; this is a perfectly natural and standard set of restrictions to make and does not actually diminish the set of numbers which are expressible in this format, but the restriction is not technically necessary for Lojban. Then we will denote <math>z</math> by the continued fraction representation <math>z = (a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math>; the whole rhs representation is called a string. Notice that the integer part is included. In this format, for each <math>i</math>, "<math>a_i : b_i</math>" forms a single unit called a macrodigit; for each <math>i</math>, "<math>a_i</math>" and "<math>b_i</math>" each are microdigits; the colon ("<math>:</math>") separates microdigits and the comma ("<math>,</math>") separates macrodigits. Microdigits can be expressed in any base or other representation and macrodigits could be reversed or slightly rearranged (such as being of form "<math>b_i : a_{(i+1)}</math>"; however, for our purposes here microdigits will be expressed in big-endian traditional decimal and macrodigits will be formed and ordered as shown; the specification herein proposed will obligate the user to express the macrodigits in the form which is shown (id est: of form "<math>a_i : b_i</math>"; within any given macrodigit, the first microdigit expressed represents <math>a_i</math> and the second (and final) microdigit expressed represents <math>b_i</math>, only) but the other features aforementioned are not guaranteed, although they may normally be assumed as a contextless default. In order to be clear: in this representation, each macrodigit will consist of exactly two microdigits - namely, <math>a_i</math> and <math>b_i</math> in that order, for all <math>i</math> - and these microdigits will be separated explicitly by "pi'e"; meanwhile, macrodigits will be separated explicitly by "pi". In this representation, I will denote a not-explicitly-specified microdigit by a pair of consecutive underscores ("<math>\_\_</math>"). In the 'big-endian' arrangement of the macrodigits (as herein depicted), the first microdigit (<math>a_0</math>) represents the 'integer part' of the expression.<br />
<br />
In this system, let "pi'e" represent ":" and let "pi" represent ",", each bijectively. Then the basic method of expressing a continued fraction is to just read <math>(a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math> where each microdigit is expressed in some base which represents integers, the parenthesis are not mentioned, the separators being named/pronounced as before, "ra'e" being used in order to create cyclic patterns or to extend the string indefinitely, and the string being terminated as any numeral string could or would be. The interpretation of the whole string according to these rules for continued fractions would be specified via JUhAU.<br />
<br />
A string terminates if and only if "ra'e" is not explicitly used. "ra'e" will couple with exactly one microdigit, and exactly every following explicitly mentioned microdigit in that position of their macrodigits will be considered to be part of a repetitious sequence applying to/running over the microdigits in that position of their macrodigits; the other microdigit is unaffected by it. Moreover, it can couple with "pi'e" as well (see below), but this occurs iff "ra'e" is explicitly mentioned immediately prior to exactly an explicitly mentioned "pi'e". If it couples with <math>a_j</math> for some <math>j</math>, then it will cyclically repeat that <math>a_j</math> and all explicitly mentioned <math>a_{(j+k)}</math> for all <math>k>0</math> in each <math>a_i</math> spot until the last <math>b_i</math> (which either will be explicitly mentioned and defined as last by the closure of the string scope (formally, all subsequent <math>b_i</math> will be trivial), or will be nonexistent according to the next point); iff it couples with <math>b_j</math> for some <math>j</math>, then the string is extended to infinite length and there exists no 'last <math>b_i</math>' (meaning that any repetition on <math>a_i</math> will also continue ad infinitum).<br />
Thus, <math>(a_0:b_0, a_1:b_1, \operatorname{ra'e} a_2:b_2, a_3:b_3, \_\_:b_4, \_\_:b_5, \_\_:b_6, \dots, \_\_:b_{10}, \_\_:\operatorname{ra'e} b_{11}) = (a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, a_2:b_4, a_3:b_5, a_2:b_6, a_3:b_7, a_2:b_8, a_3:b_9, a_2:b_{10}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, \dots)</math>.<br />
<br />
Additional rules:<br />
* For any <math>i>0</math>, if <math>a_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math>. These are called "context-dependent defaults". <math>a_0 = 0</math> if it is not explicitly mentioned unless context very clearly indicates otherwise.<br />
* For any <math>i</math>, if <math>b_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math> if the string continues (explicitly or by sufficient "ra'e") and <math>0</math> otherwise. This is especially true if the verbal expression of the string is terminated and "ra'e" was not explicitly used (on <math>b_j</math> for some <math>j</math>): all finite strings can infinitely extended by right-concatenating "<math>1:0, 1:0, 1:0, \dots)</math> to them (this is similar to decimal notation; for example: <math>8.23 = 8.23000\dots</math>). These are called "context-dependent defaults".<br />
* If exactly one microdigit is explicitly mentioned in a given macrodigit, then: it is to be understood to be <math>a_i</math> iff "ra'e" did not couple with "pi'e"; regardless of the prior presence of "ra'e pi'e" in the string, the implicit microdigit will assume the generic default value or (preferably) the value according to a repetition or formula which it inherited (see the aforementioned context-dependent defaults).<br />
<br />
Even though the basic and assumed notation for <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> is <math>(a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, \dots)</math> (this is so-called 'big-endian' in the macrodigits), other formats can be supported iff they are explicitly specified. For example, with a change of endianness in the macrodigits, <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, a_3:b_3, a_2:b_2, a_1:b_1, a_0:b_0)</math>. It is also reasonable that the microdigits could be reordered (note that this is not a change in the endianness of each microdigit (which would change <math>12:34</math> to <math>21:43</math>); rather, it is a transposition of the microdigits within each macrodigit) like so: <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, b_3:a_3, b_2:a_2, b_1:a_1, b_0:a_0)</math>; notice that in this example, I also changed the endianness of the macrodigits because the expression does not make much intuitive sense otherwise (but it would nonetheless be possible to do merely one of these changes in isolation, even if it is not advisable or sensical).<br />
<br />
The string will terminate and be interpreted as a number formed from the specified continued fraction as all other digits strings do (see my other work).<br />
<br />
-- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 08:10, 9 March 2018 (UTC)<br />
<br />
== Alternative Explanation ==<br />
<br />
The description in this section is intended to provide the same results as those in the "Original Explanation" section.<br />
<br />
Zeroth, the mode must be activated (as described previously).<br />
<br />
=== Step 1: Simplest (and Finite) Case ===<br />
<br />
Let <math>n \in \mathbb{N} \cup \{0\}</math>. Consider the continued fraction <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>\forall i, a_i</math> & <math>b_i</math> will be explicitly defined, particularly as they arise. We can enforce conditions on the sequences <math>(a_i)_i</math> & <math>(b_i)_i</math>, but we will ignore such details, because we just need formal continued fractions.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=Proposal:_Digit_Strings_which_Represent_Continued_Fractions&diff=122690Proposal: Digit Strings which Represent Continued Fractions2018-03-16T19:25:27Z<p>Krtisfranks: </p>
<hr />
<div>{{jbocre/en}}<br />
<br />
This article is a proposed description of a means by which to express numbers in a generalized continued fraction format as represented by a string of digits. It will not discuss other notations for continued fractions. By way of analogy, the subject matter of this article would be similar to a description of the decimal system (base) and will not touch on subject matter which is similar to means of expressing numbers as summations (big operator "<math>\sum</math>") or formal polynomials in <math>10</math> with coefficients in <math>\mathbb{Z} \cap [0,9]</math>, even though all of these are mutually equivalent.<br />
<br />
For the purposes of this article: All expressions are big-endian and microdigits are in traditional decimal. PEMDAS is obeyed.<br />
<br />
== Mode Activation ==<br />
<br />
== Original Explanation ==<br />
<br />
Let <math>z = a_0 + b_0/(a_1 + b_1/(a_2 + b_2/(\dots))) = a_0 + \underset{i=0}{\overset{\infty}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>a_i</math> and <math>b_i</math> are integers for all <math>i</math> (see [https://oeis.org/wiki/Continued_fractions#Gauss.27_Kettenbruch_notation Kettenbruch notation here]). In fact, for all i, we will canonically restrict <math>a_{(i+1)}</math> and <math>b_i</math> to nonnegative integers such that if <math>b_j = 0</math>, then <math>a_k = 1</math> and <math>b_k = 0</math> for all <math>k \geq j</math>; this is a perfectly natural and standard set of restrictions to make and does not actually diminish the set of numbers which are expressible in this format, but the restriction is not technically necessary for Lojban. Then we will denote <math>z</math> by the continued fraction representation <math>z = (a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math>; the whole rhs representation is called a string. Notice that the integer part is included. In this format, for each <math>i</math>, "<math>a_i : b_i</math>" forms a single unit called a macrodigit; for each <math>i</math>, "<math>a_i</math>" and "<math>b_i</math>" each are microdigits; the colon ("<math>:</math>") separates microdigits and the comma ("<math>,</math>") separates macrodigits. Microdigits can be expressed in any base or other representation and macrodigits could be reversed or slightly rearranged (such as being of form "<math>b_i : a_{(i+1)}</math>"; however, for our purposes here microdigits will be expressed in big-endian traditional decimal and macrodigits will be formed and ordered as shown; the specification herein proposed will obligate the user to express the macrodigits in the form which is shown (id est: of form "<math>a_i : b_i</math>"; within any given macrodigit, the first microdigit expressed represents <math>a_i</math> and the second (and final) microdigit expressed represents <math>b_i</math>, only) but the other features aforementioned are not guaranteed, although they may normally be assumed as a contextless default. In order to be clear: in this representation, each macrodigit will consist of exactly two microdigits - namely, <math>a_i</math> and <math>b_i</math> in that order, for all <math>i</math> - and these microdigits will be separated explicitly by "pi'e"; meanwhile, macrodigits will be separated explicitly by "pi". In this representation, I will denote a not-explicitly-specified microdigit by a pair of consecutive underscores ("<math>\_\_</math>"). In the 'big-endian' arrangement of the macrodigits (as herein depicted), the first microdigit (<math>a_0</math>) represents the 'integer part' of the expression.<br />
<br />
In this system, let "pi'e" represent ":" and let "pi" represent ",", each bijectively. Then the basic method of expressing a continued fraction is to just read <math>(a_0 : b_0, a_1 : b_1, a_2 : b_2, \dots)</math> where each microdigit is expressed in some base which represents integers, the parenthesis are not mentioned, the separators being named/pronounced as before, "ra'e" being used in order to create cyclic patterns or to extend the string indefinitely, and the string being terminated as any numeral string could or would be. The interpretation of the whole string according to these rules for continued fractions would be specified via JUhAU.<br />
<br />
A string terminates if and only if "ra'e" is not explicitly used. "ra'e" will couple with exactly one microdigit, and exactly every following explicitly mentioned microdigit in that position of their macrodigits will be considered to be part of a repetitious sequence applying to/running over the microdigits in that position of their macrodigits; the other microdigit is unaffected by it. Moreover, it can couple with "pi'e" as well (see below), but this occurs iff "ra'e" is explicitly mentioned immediately prior to exactly an explicitly mentioned "pi'e". If it couples with <math>a_j</math> for some <math>j</math>, then it will cyclically repeat that <math>a_j</math> and all explicitly mentioned <math>a_{(j+k)}</math> for all <math>k>0</math> in each <math>a_i</math> spot until the last <math>b_i</math> (which either will be explicitly mentioned and defined as last by the closure of the string scope (formally, all subsequent <math>b_i</math> will be trivial), or will be nonexistent according to the next point); iff it couples with <math>b_j</math> for some <math>j</math>, then the string is extended to infinite length and there exists no 'last <math>b_i</math>' (meaning that any repetition on <math>a_i</math> will also continue ad infinitum).<br />
Thus, <math>(a_0:b_0, a_1:b_1, \operatorname{ra'e} a_2:b_2, a_3:b_3, \_\_:b_4, \_\_:b_5, \_\_:b_6, \dots, \_\_:b_{10}, \_\_:\operatorname{ra'e} b_{11}) = (a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, a_2:b_4, a_3:b_5, a_2:b_6, a_3:b_7, a_2:b_8, a_3:b_9, a_2:b_{10}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, a_3:b_{11}, a_2:b_{11}, \dots)</math>.<br />
<br />
Additional rules:<br />
* For any <math>i</math>, if <math>a_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math>. These are called "context-dependent defaults".<br />
* For any <math>i</math>, if <math>b_i</math> is not explicitly mentioned, then it is assumed to take on the appropriate value according to an ongoing formula which applies to it (such as by "ra'e") or, otherwise, it defaults to <math>1</math> if the string continues (explicitly or by sufficient "ra'e") and <math>0</math> otherwise. This is especially true if the verbal expression of the string is terminated and "ra'e" was not explicitly used (on <math>b_j</math> for some <math>j</math>): all finite strings can infinitely extended by right-concatenating "<math>1:0, 1:0, 1:0, \dots)</math> to them (this is similar to decimal notation; for example: <math>8.23 = 8.23000\dots</math>). These are called "context-dependent defaults".<br />
* If exactly one microdigit is explicitly mentioned in a given macrodigit, then: it is to be understood to be <math>a_i</math> iff "ra'e" did not couple with "pi'e"; regardless of the prior presence of "ra'e pi'e" in the string, the implicit microdigit will assume the generic default value or (preferably) the value according to a repetition or formula which it inherited (see the aforementioned context-dependent defaults).<br />
<br />
Even though the basic and assumed notation for <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math> is <math>(a_0:b_0, a_1:b_1, a_2:b_2, a_3:b_3, \dots)</math> (this is so-called 'big-endian' in the macrodigits), other formats can be supported iff they are explicitly specified. For example, with a change of endianness in the macrodigits, <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, a_3:b_3, a_2:b_2, a_1:b_1, a_0:b_0)</math>. It is also reasonable that the microdigits could be reordered (note that this is not a change in the endianness of each microdigit (which would change <math>12:34</math> to <math>21:43</math>); rather, it is a transposition of the microdigits within each macrodigit) like so: <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big) = (\dots, b_3:a_3, b_2:a_2, b_1:a_1, b_0:a_0)</math>; notice that in this example, I also changed the endianness of the macrodigits because the expression does not make much intuitive sense otherwise (but it would nonetheless be possible to do merely one of these changes in isolation, even if it is not advisable or sensical).<br />
<br />
The string will terminate and be interpreted as a number formed from the specified continued fraction as all other digits strings do (see my other work).<br />
<br />
-- [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 08:10, 9 March 2018 (UTC)<br />
<br />
== Alternative Explanation ==<br />
<br />
The description in this section is intended to provide the same results as those in the "Original Explanation" section.<br />
<br />
Zeroth, the mode must be activated (as described previously).<br />
<br />
=== Step 1: Simplest (and Finite) Case ===<br />
<br />
Let <math>n \in \mathbb{N} \cup \{0\}</math>. Consider the continued fraction <math>a_0 + \underset{i=0}{\overset{n}{\mathrm K}} \big(\frac{b_i}{a_{i+1}}\big)</math>, where <math>\forall i, a_i</math> & <math>b_i</math> will be explicitly defined, particularly as they arise. We can enforce conditions on the sequences <math>(a_i)_i</math> & <math>(b_i)_i</math>, but we will ignore such details, because we just need formal continued fractions.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=ISO-generated_fu%27ivla_for_scripts&diff=122689ISO-generated fu'ivla for scripts2018-03-14T02:13:35Z<p>Krtisfranks: /* Source Standard and Paradigm */</p>
<hr />
<div>krtisfránks proposes the adoption of a convention for easily naming scripts in Lojban. Moreover, it is suggested that the convention follow the [[ISO generated cultural fu'ivla|paradigm established for other ISO-generated fu'ivla]] (to which there shall be repeated reference in this article).<br />
<br />
== Source Standard and Paradigm ==<br />
<br />
The proposed source material would be ISO 15924, probably the Alpha-4 codes. The codes must (and should) be spelled with only basic Latin characters.<br />
<br />
The paradigm will be that which is referenced [[ISO generated cultural fu'ivla|here]].<br />
<br />
== Complications ==<br />
<br />
There are minor complications.<br />
<br />
=== #1: Length ===<br />
<br />
First, the Alpha-4 codes are long, especially compared to the codes for countries, languages, and currencies which each produce codes of (at most, for our purposes) three letters in length; however, this <u>is</u> the standard and no reasonable alternative exists (at least in ISO). Thus, we pretty much just need to accept them. We could go with the numerical codes instead, but that would be more difficult to remember and to produce on the fly and would require the creation of a new (non-conflicting) system. (By the way, we should probably develop such a system in any case, but I will hereinafter assume an Alpha-''n'' code.)<br />
<br />
=== #2: Capitalization ===<br />
<br />
Second, exactly the first letter in the codes is capitalized for scripts unlike the other codes which are monotone in casing or do not seem to care. krtisfránks is not yet sure if this is a requirement of the standard. If it is, then we can ignore this issue because any output from the borrowing algorithm will just be assumed to follow this rule (wherein the first letter is capital and all others are lowercase). If not, then we must address this convention. In any case, if really desired, we could create an additional syllable that indicates the capitalization of exactly the next letter (the others defaulting to lowercase). This could be useful for sticklers who want to be careful with all codes or for use with comes wherein capitalization is important.<br />
<br />
If anyone can provide more information, please do so here.<br />
<br />
==== Update ====<br />
<br />
<br />
'''UPDATE:''' According to expert and registrar by the ISO 15924 Registration Authority, Michael Everson, the casing does ''NOT'' matter. For more information check [https://drive.google.com/open?id=1qps5n78DSzc6BioDN9dCWF3sUqFlzSin the content of this link]. Any mention of casing throughout the rest of this article should be ignored; the algorithm which converts ISO 15924 (Alpha) codes to Lojban fu'ivla or back will not take casing into account; all letters in the ISO 15924 Alpha code will bijectively map to the same (phonotactic-context-dependent) string of lerfu (either 'Cu', 'Ce', 'V', or 'hV') in the Lojban fu'ivla, regardless of the casing with which they are conventionally given/displayed in indices or registration files. So, for example, "Zmth", "zmth", "zMth", "ZMTH", etc. will all map to "zumutuxe", regardless of which letters in the ISO code name/string are capital and which are lowercase; meanwhile, each of those ISO code names/strings shall be considered equivalent and "zumutuxe" shall map back to them all. - [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 01:25, 14 March 2018 (UTC)<br />
<br />
=== #3: Introducer Selection ===<br />
<br />
Third, and this is the important one, we have to choose an appropriate gismu as the introducer. Three options immediately come to mind: "ciska", "lerfu", and "cilfu".<br />
<br />
* "ciska" is not entirely appropriate since it cares about the writer, the medium, and the ink in addition to what is actually written. Even then, it is really about the writing itself rather than the system of symbols that is being employed. It does have a cmarafsi which might be nice but it is not overly useful.<br />
* "lerfu" is pretty nice. It would be better if we could use "selyle'u", but at least the relationship is there. The downsides are that it ends with "-u", making it potentially confusing or garden-pathing since the letters in the code will usually be turned into syllables of the form '-Cu-'. For example, "lerfuzumutuxe" (Zmth) might be confused for "Fzmt... oh, there is an 'h'...". Also, if we ever want to name individual symbols using an introducer (such as borrowing from Unicode or random names), the two conventions in Lojban would at least be confusing with one another - and they could easily conflict or lead to garden-pathing. There might already be zi'evla which cause such problems. The upside is that there are cmarafsi, so the word length can be reduced and we can more closely follow the model of "bangu"-introduced borrowings, rather than "gugde"-introduced ones. (But we would have to adapt since "lerfu" is not as versatile as "bangu". This is a small technical matter. The cmarafsi of "lerfu" are much nicer than of "ciska".)<br />
* "cilfu" does not have the problem with semantics that the "ciska" and "lerfu" have; it definitely means "script" and can only mean that (no need to worry about borrowing names for individual symbols). It suffers from the terminal "-u" issue though. It also has no cmarafsi. And it is redundant. Why create a fu'ivla when a link-sumti construct would do? On the other hand, this redundancy could be viewed as making this word the prime candidate for the job. (I (krtisfránks) do think that the codes should be borrowed; so, if the job must be done, maybe this is the best way to do it.)<br />
<br />
krtisfránks personally likes "lerfu" or "cilfu" for this role (in increasing order of preference). Perhaps if their final vowels were edited ("''lerfa''-"? "''cilfe''-"?), then they would be better. Then it is a matter of choosing either redundancy and word length versus potential conflicts with future borrowings and improper semantics.<br />
<br />
An alternative would be to let the introducer be "''slerfa''-" (or something similar) for "selyle'u" and correcting the terminal "-u"; this might even lend itself to shorter words in some situations (by using "''sler(f)''-"). The bad news about this option is the fact that a word (and not just a rafsi-like fragment) called "slerfa" (or whatever) could come to be created (yes, I know that "slerfa" is not itself a Lojban word even in possibility - but I am using "slerfa" as a placeholder here), which would then conflict with the motivations of this proposal. We could book the word in order to pre-empt this possibility, but it would be a bit of a waste of brivla space.<br />
<br />
In any case, after the introducer is selected, assuming that the first two issues raised are resolved nicely, the translation algorithm is the same as the rest and is ready to go.<br />
<br />
Additionally, the introducer cannot end with "y".<br />
<br />
==== Extra Rule ====<br />
<br />
Once we select an introducer, then we should forbid the creation of any brivla which consists of or contains that introducer(s) followed by (concatenated with) anything other than a string which does not contain a consonant cluster within that substring's first four lerfu, unless the brivla is a zi'evla or lujvo which is explicitly and (in a reasonable way) semantically derived from a fu'ivla produced by this algorithm (and, in the case of lujvo, the valsi produced by this algorithm should be a veljvo and it or a mutation of it should be acting as a rafsi). rafsi are allowed if used appropriately.<br />
<br />
For example: Suppose that we choose "cilfa-" to be the introducer string. Then we outlaw the creation of any brivla which begins with or contains the substring "cilfaX<sub>1</sub>X<sub>2</sub>X<sub>3</sub>X<sub>4</sub>", where X<sub>i</sub> is any Lojban lerfu (not counting .y'y, which is optionally included with the selection of any vowel), unless X<sub>j</sub> and X<sub>(j+1)</sub> are both consonants (where j is an integer such that 0<j<4) or the resulting word in total is a derivative of a word generated by this algorithm.<br />
<br />
This might interfere with the creation of unrelated lujvo (such as "cilfau"). I suppose that we would have to exempt out non-zi'evla-veljvo lujvo.<br />
<br />
Similar rules should be implemented for the other ISO-generated fu'ivla.<br />
<br />
== Mapping ==<br />
<br />
(This is the same as in the results described [[ISO generated cultural fu'ivla|here]]).<br />
<br />
Each vowel V (except "Y"/"y") will be mapped to ''V'' if it is the first letter in the code and does not immediately follow a vowel, and to ''`V'' (id est: ''hV'') if it is any subsequent letter in the code or immediately follows a vowel.<br />
<br />
Each consonant C (except for "H"/"h", "Q"/"q", and "W"/"w") will map to ''Cu''. This is regardless of their pronunciation in English, French, Latin, or the language that motivated the ISO code designation.<br />
<br />
The aforementioned exceptions are handled thusly:<br />
* "Y"/"y" will map to ''je''.<br />
* "H"/"h" will map to ''xe''.<br />
* "Q"/"q" will map to ''ke''.<br />
* "W"/"w" will map to ''ve''.<br />
<br />
== Examples ==<br />
<br />
The aforementioned issues can be resolved by various assumptions; what follows is a series of examples representing different such resolutions. It is not meant to be complete, only demonstrative.<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
<br />
=== Type A ===<br />
<br />
Assume that: 1) Alpha-4 codes are used; 2) Casing does not matter; 3) "lerfu" is used as the introducer (<u>'''this is the biggest caveat to this example'''</u>).<br />
<br />
Then:<br />
*The introducer is "''ler''-" unless the code begins with a vowel (other than "Y"), an "F", or an "R".<br />
*In the case of an initial vowel (other than "Y"), the introducer is "''lerf''-".<br />
*If the code begins with an "F", then the introducer is "''le'ur''-".<br />
*If the code begins with an "R", then the introducer is "''le'un''-".<br />
<br />
<br />
<br />
The name for the script described/named as '''Mathematical Notation''', which is assigned code ''''Zmth'''', would be "'''lerzumutuxe'''". More illustratively:<br />
<br />
Normal examples:<br />
*Aaaa -> lerfa'a'a'a.<br />
*Abaa -> lerfabu'a'a.<br />
*Baaa -> lerbu'a'a'a.<br />
*Bbbb -> lerbubububu.<br />
<br />
"F"-initial examples:<br />
*Faaa -> le'urfu'a'a'a.<br />
*Fbaa -> le'urfubu'a'a.<br />
*Fbbb -> le'urfubububu.<br />
<br />
"R"-initial examples:<br />
*Raaa -> le'unru'a'a'a.<br />
*Rbaa -> le'unrubu'a'a.<br />
*Rbbb -> le'unrubububu.<br />
<br />
<br />
<br />
Note: I think that the case of initial "U" should be handled just fine under this system, but the audience will need to take care in interpreting such words.<br />
<br />
<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
*In particular, I am not advocating for the adoption of "lerfu" as the introducer.<br />
<br />
=== Type B ===<br />
<br />
Assume that: 1) Alpha-4 codes are used; 2) Casing does not matter; 3) "''cilfe''-" (derived from "cilfu") is used as the introducer (<u>'''this is the biggest caveat to this example'''</u>).<br />
<br />
Then:<br />
*The output follows the pattern of the ISO-generated country names.<br />
*The introducer is "''cilfe''-" unless the code begins with a non-"Y" vowel.<br />
*In the case of an initial vowel (excepting "Y"), the introducer is "''cilfe`''-"; note the presence of the .y'y.<br />
<br />
<br />
<br />
The name for the script described/named as '''Mathematical Notation''', which is assigned code ''''Zmth'''', would be "'''cilfezumutuxe'''". More illustratively:<br />
<br />
Normal examples:<br />
*Aaaa -> cilfe'a'a'a'a.<br />
*Abaa -> cilfe'abu'a'a.<br />
*Baaa -> cilfebu'a'a'a.<br />
*Bbbb -> cilfebubububu.<br />
<br />
<br />
<br />
Note: A minor disappointment with this method is that "cilfe" is not a Lojban word. The good news is that, by gismu similarity conflict with "cilfu", it presently cannot be - thus (for the time being), we do not need to worry about "cilfe" being defined in some way contrary to this proposal's motivations and semantics.<br />
<br />
This method has the following advantage over the Type A method proposal: Very little case-worrying is necessary, words may be generated easily and with little thought. The only issue that is of concern is that of initial vowels being handled appropriately. But, since forgetting the .y'y will phonotactically break the word in all but at most two cases anyway (these being initial "I" and possibly initial "U" in future versions of Lojban), spotting these errors/troubles should not be too difficult. It is not only regular, but simple as well.<br />
<br />
The cost relative to the Type A proposal is that all output words will be at least as long from this method as from that method. Some elegance may be felt to be lost also.<br />
<br />
<br />
<br />
<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
*In particular, I am not advocating for the adoption of "''cilfe''" as the introducer.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=ISO-generated_fu%27ivla_for_scripts&diff=122688ISO-generated fu'ivla for scripts2018-03-14T02:02:00Z<p>Krtisfranks: /* Extra Rule */</p>
<hr />
<div>krtisfránks proposes the adoption of a convention for easily naming scripts in Lojban. Moreover, it is suggested that the convention follow the [[ISO generated cultural fu'ivla|paradigm established for other ISO-generated fu'ivla]] (to which there shall be repeated reference in this article).<br />
<br />
== Source Standard and Paradigm ==<br />
<br />
The proposed source material would be ISO 15924, probably the Alpha-4 codes.<br />
<br />
The paradigm will be that which is referenced [[ISO generated cultural fu'ivla|here]].<br />
<br />
== Complications ==<br />
<br />
There are minor complications.<br />
<br />
=== #1: Length ===<br />
<br />
First, the Alpha-4 codes are long, especially compared to the codes for countries, languages, and currencies which each produce codes of (at most, for our purposes) three letters in length; however, this <u>is</u> the standard and no reasonable alternative exists (at least in ISO). Thus, we pretty much just need to accept them. We could go with the numerical codes instead, but that would be more difficult to remember and to produce on the fly and would require the creation of a new (non-conflicting) system. (By the way, we should probably develop such a system in any case, but I will hereinafter assume an Alpha-''n'' code.)<br />
<br />
=== #2: Capitalization ===<br />
<br />
Second, exactly the first letter in the codes is capitalized for scripts unlike the other codes which are monotone in casing or do not seem to care. krtisfránks is not yet sure if this is a requirement of the standard. If it is, then we can ignore this issue because any output from the borrowing algorithm will just be assumed to follow this rule (wherein the first letter is capital and all others are lowercase). If not, then we must address this convention. In any case, if really desired, we could create an additional syllable that indicates the capitalization of exactly the next letter (the others defaulting to lowercase). This could be useful for sticklers who want to be careful with all codes or for use with comes wherein capitalization is important.<br />
<br />
If anyone can provide more information, please do so here.<br />
<br />
==== Update ====<br />
<br />
<br />
'''UPDATE:''' According to expert and registrar by the ISO 15924 Registration Authority, Michael Everson, the casing does ''NOT'' matter. For more information check [https://drive.google.com/open?id=1qps5n78DSzc6BioDN9dCWF3sUqFlzSin the content of this link]. Any mention of casing throughout the rest of this article should be ignored; the algorithm which converts ISO 15924 (Alpha) codes to Lojban fu'ivla or back will not take casing into account; all letters in the ISO 15924 Alpha code will bijectively map to the same (phonotactic-context-dependent) string of lerfu (either 'Cu', 'Ce', 'V', or 'hV') in the Lojban fu'ivla, regardless of the casing with which they are conventionally given/displayed in indices or registration files. So, for example, "Zmth", "zmth", "zMth", "ZMTH", etc. will all map to "zumutuxe", regardless of which letters in the ISO code name/string are capital and which are lowercase; meanwhile, each of those ISO code names/strings shall be considered equivalent and "zumutuxe" shall map back to them all. - [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 01:25, 14 March 2018 (UTC)<br />
<br />
=== #3: Introducer Selection ===<br />
<br />
Third, and this is the important one, we have to choose an appropriate gismu as the introducer. Three options immediately come to mind: "ciska", "lerfu", and "cilfu".<br />
<br />
* "ciska" is not entirely appropriate since it cares about the writer, the medium, and the ink in addition to what is actually written. Even then, it is really about the writing itself rather than the system of symbols that is being employed. It does have a cmarafsi which might be nice but it is not overly useful.<br />
* "lerfu" is pretty nice. It would be better if we could use "selyle'u", but at least the relationship is there. The downsides are that it ends with "-u", making it potentially confusing or garden-pathing since the letters in the code will usually be turned into syllables of the form '-Cu-'. For example, "lerfuzumutuxe" (Zmth) might be confused for "Fzmt... oh, there is an 'h'...". Also, if we ever want to name individual symbols using an introducer (such as borrowing from Unicode or random names), the two conventions in Lojban would at least be confusing with one another - and they could easily conflict or lead to garden-pathing. There might already be zi'evla which cause such problems. The upside is that there are cmarafsi, so the word length can be reduced and we can more closely follow the model of "bangu"-introduced borrowings, rather than "gugde"-introduced ones. (But we would have to adapt since "lerfu" is not as versatile as "bangu". This is a small technical matter. The cmarafsi of "lerfu" are much nicer than of "ciska".)<br />
* "cilfu" does not have the problem with semantics that the "ciska" and "lerfu" have; it definitely means "script" and can only mean that (no need to worry about borrowing names for individual symbols). It suffers from the terminal "-u" issue though. It also has no cmarafsi. And it is redundant. Why create a fu'ivla when a link-sumti construct would do? On the other hand, this redundancy could be viewed as making this word the prime candidate for the job. (I (krtisfránks) do think that the codes should be borrowed; so, if the job must be done, maybe this is the best way to do it.)<br />
<br />
krtisfránks personally likes "lerfu" or "cilfu" for this role (in increasing order of preference). Perhaps if their final vowels were edited ("''lerfa''-"? "''cilfe''-"?), then they would be better. Then it is a matter of choosing either redundancy and word length versus potential conflicts with future borrowings and improper semantics.<br />
<br />
An alternative would be to let the introducer be "''slerfa''-" (or something similar) for "selyle'u" and correcting the terminal "-u"; this might even lend itself to shorter words in some situations (by using "''sler(f)''-"). The bad news about this option is the fact that a word (and not just a rafsi-like fragment) called "slerfa" (or whatever) could come to be created (yes, I know that "slerfa" is not itself a Lojban word even in possibility - but I am using "slerfa" as a placeholder here), which would then conflict with the motivations of this proposal. We could book the word in order to pre-empt this possibility, but it would be a bit of a waste of brivla space.<br />
<br />
In any case, after the introducer is selected, assuming that the first two issues raised are resolved nicely, the translation algorithm is the same as the rest and is ready to go.<br />
<br />
Additionally, the introducer cannot end with "y".<br />
<br />
==== Extra Rule ====<br />
<br />
Once we select an introducer, then we should forbid the creation of any brivla which consists of or contains that introducer(s) followed by (concatenated with) anything other than a string which does not contain a consonant cluster within that substring's first four lerfu, unless the brivla is a zi'evla or lujvo which is explicitly and (in a reasonable way) semantically derived from a fu'ivla produced by this algorithm (and, in the case of lujvo, the valsi produced by this algorithm should be a veljvo and it or a mutation of it should be acting as a rafsi). rafsi are allowed if used appropriately.<br />
<br />
For example: Suppose that we choose "cilfa-" to be the introducer string. Then we outlaw the creation of any brivla which begins with or contains the substring "cilfaX<sub>1</sub>X<sub>2</sub>X<sub>3</sub>X<sub>4</sub>", where X<sub>i</sub> is any Lojban lerfu (not counting .y'y, which is optionally included with the selection of any vowel), unless X<sub>j</sub> and X<sub>(j+1)</sub> are both consonants (where j is an integer such that 0<j<4) or the resulting word in total is a derivative of a word generated by this algorithm.<br />
<br />
This might interfere with the creation of unrelated lujvo (such as "cilfau"). I suppose that we would have to exempt out non-zi'evla-veljvo lujvo.<br />
<br />
Similar rules should be implemented for the other ISO-generated fu'ivla.<br />
<br />
== Mapping ==<br />
<br />
(This is the same as in the results described [[ISO generated cultural fu'ivla|here]]).<br />
<br />
Each vowel V (except "Y"/"y") will be mapped to ''V'' if it is the first letter in the code and does not immediately follow a vowel, and to ''`V'' (id est: ''hV'') if it is any subsequent letter in the code or immediately follows a vowel.<br />
<br />
Each consonant C (except for "H"/"h", "Q"/"q", and "W"/"w") will map to ''Cu''. This is regardless of their pronunciation in English, French, Latin, or the language that motivated the ISO code designation.<br />
<br />
The aforementioned exceptions are handled thusly:<br />
* "Y"/"y" will map to ''je''.<br />
* "H"/"h" will map to ''xe''.<br />
* "Q"/"q" will map to ''ke''.<br />
* "W"/"w" will map to ''ve''.<br />
<br />
== Examples ==<br />
<br />
The aforementioned issues can be resolved by various assumptions; what follows is a series of examples representing different such resolutions. It is not meant to be complete, only demonstrative.<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
<br />
=== Type A ===<br />
<br />
Assume that: 1) Alpha-4 codes are used; 2) Casing does not matter; 3) "lerfu" is used as the introducer (<u>'''this is the biggest caveat to this example'''</u>).<br />
<br />
Then:<br />
*The introducer is "''ler''-" unless the code begins with a vowel (other than "Y"), an "F", or an "R".<br />
*In the case of an initial vowel (other than "Y"), the introducer is "''lerf''-".<br />
*If the code begins with an "F", then the introducer is "''le'ur''-".<br />
*If the code begins with an "R", then the introducer is "''le'un''-".<br />
<br />
<br />
<br />
The name for the script described/named as '''Mathematical Notation''', which is assigned code ''''Zmth'''', would be "'''lerzumutuxe'''". More illustratively:<br />
<br />
Normal examples:<br />
*Aaaa -> lerfa'a'a'a.<br />
*Abaa -> lerfabu'a'a.<br />
*Baaa -> lerbu'a'a'a.<br />
*Bbbb -> lerbubububu.<br />
<br />
"F"-initial examples:<br />
*Faaa -> le'urfu'a'a'a.<br />
*Fbaa -> le'urfubu'a'a.<br />
*Fbbb -> le'urfubububu.<br />
<br />
"R"-initial examples:<br />
*Raaa -> le'unru'a'a'a.<br />
*Rbaa -> le'unrubu'a'a.<br />
*Rbbb -> le'unrubububu.<br />
<br />
<br />
<br />
Note: I think that the case of initial "U" should be handled just fine under this system, but the audience will need to take care in interpreting such words.<br />
<br />
<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
*In particular, I am not advocating for the adoption of "lerfu" as the introducer.<br />
<br />
=== Type B ===<br />
<br />
Assume that: 1) Alpha-4 codes are used; 2) Casing does not matter; 3) "''cilfe''-" (derived from "cilfu") is used as the introducer (<u>'''this is the biggest caveat to this example'''</u>).<br />
<br />
Then:<br />
*The output follows the pattern of the ISO-generated country names.<br />
*The introducer is "''cilfe''-" unless the code begins with a non-"Y" vowel.<br />
*In the case of an initial vowel (excepting "Y"), the introducer is "''cilfe`''-"; note the presence of the .y'y.<br />
<br />
<br />
<br />
The name for the script described/named as '''Mathematical Notation''', which is assigned code ''''Zmth'''', would be "'''cilfezumutuxe'''". More illustratively:<br />
<br />
Normal examples:<br />
*Aaaa -> cilfe'a'a'a'a.<br />
*Abaa -> cilfe'abu'a'a.<br />
*Baaa -> cilfebu'a'a'a.<br />
*Bbbb -> cilfebubububu.<br />
<br />
<br />
<br />
Note: A minor disappointment with this method is that "cilfe" is not a Lojban word. The good news is that, by gismu similarity conflict with "cilfu", it presently cannot be - thus (for the time being), we do not need to worry about "cilfe" being defined in some way contrary to this proposal's motivations and semantics.<br />
<br />
This method has the following advantage over the Type A method proposal: Very little case-worrying is necessary, words may be generated easily and with little thought. The only issue that is of concern is that of initial vowels being handled appropriately. But, since forgetting the .y'y will phonotactically break the word in all but at most two cases anyway (these being initial "I" and possibly initial "U" in future versions of Lojban), spotting these errors/troubles should not be too difficult. It is not only regular, but simple as well.<br />
<br />
The cost relative to the Type A proposal is that all output words will be at least as long from this method as from that method. Some elegance may be felt to be lost also.<br />
<br />
<br />
<br />
<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
*In particular, I am not advocating for the adoption of "''cilfe''" as the introducer.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=ISO-generated_fu%27ivla_for_scripts&diff=122687ISO-generated fu'ivla for scripts2018-03-14T01:51:36Z<p>Krtisfranks: /* #3: Introducer Selection */</p>
<hr />
<div>krtisfránks proposes the adoption of a convention for easily naming scripts in Lojban. Moreover, it is suggested that the convention follow the [[ISO generated cultural fu'ivla|paradigm established for other ISO-generated fu'ivla]] (to which there shall be repeated reference in this article).<br />
<br />
== Source Standard and Paradigm ==<br />
<br />
The proposed source material would be ISO 15924, probably the Alpha-4 codes.<br />
<br />
The paradigm will be that which is referenced [[ISO generated cultural fu'ivla|here]].<br />
<br />
== Complications ==<br />
<br />
There are minor complications.<br />
<br />
=== #1: Length ===<br />
<br />
First, the Alpha-4 codes are long, especially compared to the codes for countries, languages, and currencies which each produce codes of (at most, for our purposes) three letters in length; however, this <u>is</u> the standard and no reasonable alternative exists (at least in ISO). Thus, we pretty much just need to accept them. We could go with the numerical codes instead, but that would be more difficult to remember and to produce on the fly and would require the creation of a new (non-conflicting) system. (By the way, we should probably develop such a system in any case, but I will hereinafter assume an Alpha-''n'' code.)<br />
<br />
=== #2: Capitalization ===<br />
<br />
Second, exactly the first letter in the codes is capitalized for scripts unlike the other codes which are monotone in casing or do not seem to care. krtisfránks is not yet sure if this is a requirement of the standard. If it is, then we can ignore this issue because any output from the borrowing algorithm will just be assumed to follow this rule (wherein the first letter is capital and all others are lowercase). If not, then we must address this convention. In any case, if really desired, we could create an additional syllable that indicates the capitalization of exactly the next letter (the others defaulting to lowercase). This could be useful for sticklers who want to be careful with all codes or for use with comes wherein capitalization is important.<br />
<br />
If anyone can provide more information, please do so here.<br />
<br />
==== Update ====<br />
<br />
<br />
'''UPDATE:''' According to expert and registrar by the ISO 15924 Registration Authority, Michael Everson, the casing does ''NOT'' matter. For more information check [https://drive.google.com/open?id=1qps5n78DSzc6BioDN9dCWF3sUqFlzSin the content of this link]. Any mention of casing throughout the rest of this article should be ignored; the algorithm which converts ISO 15924 (Alpha) codes to Lojban fu'ivla or back will not take casing into account; all letters in the ISO 15924 Alpha code will bijectively map to the same (phonotactic-context-dependent) string of lerfu (either 'Cu', 'Ce', 'V', or 'hV') in the Lojban fu'ivla, regardless of the casing with which they are conventionally given/displayed in indices or registration files. So, for example, "Zmth", "zmth", "zMth", "ZMTH", etc. will all map to "zumutuxe", regardless of which letters in the ISO code name/string are capital and which are lowercase; meanwhile, each of those ISO code names/strings shall be considered equivalent and "zumutuxe" shall map back to them all. - [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 01:25, 14 March 2018 (UTC)<br />
<br />
=== #3: Introducer Selection ===<br />
<br />
Third, and this is the important one, we have to choose an appropriate gismu as the introducer. Three options immediately come to mind: "ciska", "lerfu", and "cilfu".<br />
<br />
* "ciska" is not entirely appropriate since it cares about the writer, the medium, and the ink in addition to what is actually written. Even then, it is really about the writing itself rather than the system of symbols that is being employed. It does have a cmarafsi which might be nice but it is not overly useful.<br />
* "lerfu" is pretty nice. It would be better if we could use "selyle'u", but at least the relationship is there. The downsides are that it ends with "-u", making it potentially confusing or garden-pathing since the letters in the code will usually be turned into syllables of the form '-Cu-'. For example, "lerfuzumutuxe" (Zmth) might be confused for "Fzmt... oh, there is an 'h'...". Also, if we ever want to name individual symbols using an introducer (such as borrowing from Unicode or random names), the two conventions in Lojban would at least be confusing with one another - and they could easily conflict or lead to garden-pathing. There might already be zi'evla which cause such problems. The upside is that there are cmarafsi, so the word length can be reduced and we can more closely follow the model of "bangu"-introduced borrowings, rather than "gugde"-introduced ones. (But we would have to adapt since "lerfu" is not as versatile as "bangu". This is a small technical matter. The cmarafsi of "lerfu" are much nicer than of "ciska".)<br />
* "cilfu" does not have the problem with semantics that the "ciska" and "lerfu" have; it definitely means "script" and can only mean that (no need to worry about borrowing names for individual symbols). It suffers from the terminal "-u" issue though. It also has no cmarafsi. And it is redundant. Why create a fu'ivla when a link-sumti construct would do? On the other hand, this redundancy could be viewed as making this word the prime candidate for the job. (I (krtisfránks) do think that the codes should be borrowed; so, if the job must be done, maybe this is the best way to do it.)<br />
<br />
krtisfránks personally likes "lerfu" or "cilfu" for this role (in increasing order of preference). Perhaps if their final vowels were edited ("''lerfa''-"? "''cilfe''-"?), then they would be better. Then it is a matter of choosing either redundancy and word length versus potential conflicts with future borrowings and improper semantics.<br />
<br />
An alternative would be to let the introducer be "''slerfa''-" (or something similar) for "selyle'u" and correcting the terminal "-u"; this might even lend itself to shorter words in some situations (by using "''sler(f)''-"). The bad news about this option is the fact that a word (and not just a rafsi-like fragment) called "slerfa" (or whatever) could come to be created (yes, I know that "slerfa" is not itself a Lojban word even in possibility - but I am using "slerfa" as a placeholder here), which would then conflict with the motivations of this proposal. We could book the word in order to pre-empt this possibility, but it would be a bit of a waste of brivla space.<br />
<br />
In any case, after the introducer is selected, assuming that the first two issues raised are resolved nicely, the translation algorithm is the same as the rest and is ready to go.<br />
<br />
Additionally, the introducer cannot end with "y".<br />
<br />
==== Extra Rule ====<br />
<br />
Once we select an introducer, then we should forbid the creation of any brivla which consists of that introducer(s) followed by (concatenated with) anything other than a string which does not contain a consonant cluster within that substring's first four lerfu, unless the brivla is a zi'evla or lujvo which is explicitly and (in a reasonable way) semantically derived from a fu'ivla produced by this algorithm (and, in the case of lujvo, the valsi produced by this algorithm should be a veljvo and it or a mutation of it should be acting as a rafsi).<br />
<br />
Similar rules should be implemented for the other ISO-generated fu'ivla.<br />
<br />
== Mapping ==<br />
<br />
(This is the same as in the results described [[ISO generated cultural fu'ivla|here]]).<br />
<br />
Each vowel V (except "Y"/"y") will be mapped to ''V'' if it is the first letter in the code and does not immediately follow a vowel, and to ''`V'' (id est: ''hV'') if it is any subsequent letter in the code or immediately follows a vowel.<br />
<br />
Each consonant C (except for "H"/"h", "Q"/"q", and "W"/"w") will map to ''Cu''. This is regardless of their pronunciation in English, French, Latin, or the language that motivated the ISO code designation.<br />
<br />
The aforementioned exceptions are handled thusly:<br />
* "Y"/"y" will map to ''je''.<br />
* "H"/"h" will map to ''xe''.<br />
* "Q"/"q" will map to ''ke''.<br />
* "W"/"w" will map to ''ve''.<br />
<br />
== Examples ==<br />
<br />
The aforementioned issues can be resolved by various assumptions; what follows is a series of examples representing different such resolutions. It is not meant to be complete, only demonstrative.<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
<br />
=== Type A ===<br />
<br />
Assume that: 1) Alpha-4 codes are used; 2) Casing does not matter; 3) "lerfu" is used as the introducer (<u>'''this is the biggest caveat to this example'''</u>).<br />
<br />
Then:<br />
*The introducer is "''ler''-" unless the code begins with a vowel (other than "Y"), an "F", or an "R".<br />
*In the case of an initial vowel (other than "Y"), the introducer is "''lerf''-".<br />
*If the code begins with an "F", then the introducer is "''le'ur''-".<br />
*If the code begins with an "R", then the introducer is "''le'un''-".<br />
<br />
<br />
<br />
The name for the script described/named as '''Mathematical Notation''', which is assigned code ''''Zmth'''', would be "'''lerzumutuxe'''". More illustratively:<br />
<br />
Normal examples:<br />
*Aaaa -> lerfa'a'a'a.<br />
*Abaa -> lerfabu'a'a.<br />
*Baaa -> lerbu'a'a'a.<br />
*Bbbb -> lerbubububu.<br />
<br />
"F"-initial examples:<br />
*Faaa -> le'urfu'a'a'a.<br />
*Fbaa -> le'urfubu'a'a.<br />
*Fbbb -> le'urfubububu.<br />
<br />
"R"-initial examples:<br />
*Raaa -> le'unru'a'a'a.<br />
*Rbaa -> le'unrubu'a'a.<br />
*Rbbb -> le'unrubububu.<br />
<br />
<br />
<br />
Note: I think that the case of initial "U" should be handled just fine under this system, but the audience will need to take care in interpreting such words.<br />
<br />
<br />
<br />
<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
*In particular, I am not advocating for the adoption of "lerfu" as the introducer.<br />
<br />
=== Type B ===<br />
<br />
Assume that: 1) Alpha-4 codes are used; 2) Casing does not matter; 3) "''cilfe''-" (derived from "cilfu") is used as the introducer (<u>'''this is the biggest caveat to this example'''</u>).<br />
<br />
Then:<br />
*The output follows the pattern of the ISO-generated country names.<br />
*The introducer is "''cilfe''-" unless the code begins with a non-"Y" vowel.<br />
*In the case of an initial vowel (excepting "Y"), the introducer is "''cilfe`''-"; note the presence of the .y'y.<br />
<br />
<br />
<br />
The name for the script described/named as '''Mathematical Notation''', which is assigned code ''''Zmth'''', would be "'''cilfezumutuxe'''". More illustratively:<br />
<br />
Normal examples:<br />
*Aaaa -> cilfe'a'a'a'a.<br />
*Abaa -> cilfe'abu'a'a.<br />
*Baaa -> cilfebu'a'a'a.<br />
*Bbbb -> cilfebubububu.<br />
<br />
<br />
<br />
Note: A minor disappointment with this method is that "cilfe" is not a Lojban word. The good news is that, by gismu similarity conflict with "cilfu", it presently cannot be - thus (for the time being), we do not need to worry about "cilfe" being defined in some way contrary to this proposal's motivations and semantics.<br />
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This method has the following advantage over the Type A method proposal: Very little case-worrying is necessary, words may be generated easily and with little thought. The only issue that is of concern is that of initial vowels being handled appropriately. But, since forgetting the .y'y will phonotactically break the word in all but at most two cases anyway (these being initial "I" and possibly initial "U" in future versions of Lojban), spotting these errors/troubles should not be too difficult. It is not only regular, but simple as well.<br />
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The cost relative to the Type A proposal is that all output words will be at least as long from this method as from that method. Some elegance may be felt to be lost also.<br />
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<font color="red"><u>'''NOTE: THIS IS NOT AN ENDORSEMENT OF ANY OF THESE ASSUMPTIONS!'''</u></font><br />
*In particular, I am not advocating for the adoption of "''cilfe''" as the introducer.</div>Krtisfrankshttps://mw.lojban.org/index.php?title=ISO-generated_fu%27ivla_for_scripts&diff=122686ISO-generated fu'ivla for scripts2018-03-14T01:43:41Z<p>Krtisfranks: /* #2: Capitalization */</p>
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<div>krtisfránks proposes the adoption of a convention for easily naming scripts in Lojban. Moreover, it is suggested that the convention follow the [[ISO generated cultural fu'ivla|paradigm established for other ISO-generated fu'ivla]] (to which there shall be repeated reference in this article).<br />
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== Source Standard and Paradigm ==<br />
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The proposed source material would be ISO 15924, probably the Alpha-4 codes.<br />
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The paradigm will be that which is referenced [[ISO generated cultural fu'ivla|here]].<br />
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== Complications ==<br />
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There are minor complications.<br />
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=== #1: Length ===<br />
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First, the Alpha-4 codes are long, especially compared to the codes for countries, languages, and currencies which each produce codes of (at most, for our purposes) three letters in length; however, this <u>is</u> the standard and no reasonable alternative exists (at least in ISO). Thus, we pretty much just need to accept them. We could go with the numerical codes instead, but that would be more difficult to remember and to produce on the fly and would require the creation of a new (non-conflicting) system. (By the way, we should probably develop such a system in any case, but I will hereinafter assume an Alpha-''n'' code.)<br />
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=== #2: Capitalization ===<br />
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Second, exactly the first letter in the codes is capitalized for scripts unlike the other codes which are monotone in casing or do not seem to care. krtisfránks is not yet sure if this is a requirement of the standard. If it is, then we can ignore this issue because any output from the borrowing algorithm will just be assumed to follow this rule (wherein the first letter is capital and all others are lowercase). If not, then we must address this convention. In any case, if really desired, we could create an additional syllable that indicates the capitalization of exactly the next letter (the others defaulting to lowercase). This could be useful for sticklers who want to be careful with all codes or for use with comes wherein capitalization is important.<br />
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If anyone can provide more information, please do so here.<br />
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==== Update ====<br />
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'''UPDATE:''' According to expert and registrar by the ISO 15924 Registration Authority, Michael Everson, the casing does ''NOT'' matter. For more information check [https://drive.google.com/open?id=1qps5n78DSzc6BioDN9dCWF3sUqFlzSin the content of this link]. Any mention of casing throughout the rest of this article should be ignored; the algorithm which converts ISO 15924 (Alpha) codes to Lojban fu'ivla or back will not take casing into account; all letters in the ISO 15924 Alpha code will bijectively map to the same (phonotactic-context-dependent) string of lerfu (either 'Cu', 'Ce', 'V', or 'hV') in the Lojban fu'ivla, regardless of the casing with which they are conventionally given/displayed in indices or registration files. So, for example, "Zmth", "zmth", "zMth", "ZMTH", etc. will all map to "zumutuxe", regardless of which letters in the ISO code name/string are capital and which are lowercase; meanwhile, each of those ISO code names/strings shall be considered equivalent and "zumutuxe" shall map back to them all. - [[User:Krtisfranks|Krtisfranks]] ([[User talk:Krtisfranks|talk]]) 01:25, 14 March 2018 (UTC)<br />
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=== #3: Introducer Selection ===<br />
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Third, and this is the important one, we have to choose an appropriate gismu as the introducer. Three options immediately come to mind: "ciska", "lerfu", and "cilfu".<br />
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* "ciska" is not entirely appropriate since it cares about the writer, the medium, and the ink in addition to what is actually written. Even then, it is really about the writing itself rather than the system of symbols that is being employed. It does have a cmarafsi which might be nice but it is not overly useful.<br />
* "lerfu" is pretty nice. It would be better if we could use "selyle'u", but at least the relationship is there. The downsides are that it ends with "-u", making it potentially confusing or garden-pathing since the letters in the code will usually be turned into syllables of the form '-Cu-'. For example, "lerfuzumutuxe" (Zmth) might be confused for "Fzmt... oh, there is an 'h'...". Also, if we ever want to name individual symbols using an introducer (such as borrowing from Unicode or random names), the two conventions in Lojban would at least be confusing with one another - and they could easily conflict or lead to garden-pathing. There might already be zi'evla which cause such problems. The upside is that there are cmarafsi, so the word length can be reduced and we can more closely follow the model of "bangu"-introduced borrowings, rather than "gugde"-introduced ones. (But we would have to adapt since "lerfu" is not as versatile as "bangu". This is a small technical matter. The cmarafsi of "lerfu" are much nicer than of "ciska".)<br />
* "cilfu" does not have the problem with semantics that the "ciska" and "lerfu" have; it definitely means "script" and can only mean that (no need to worry about borrowing names for individual symbols). It suffers from the terminal "-u" issue though. It also has no cmarafsi. And it is redundant. Why create a fu'ivla when a link-sumti construct would do? On the other hand, this redundancy could be viewed as making this word the prime candidate for the job. (I (krtisfránks) do think that the codes should be borrowed; so, if the job must be done, maybe this is the best way to do it.)<br />
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krtisfránks personally likes "lerfu" or "cilfu" for this role (in increasing order of preference). Perhaps if their final vowels were edited ("''lerfa''-"? "''cilfe''-"?), then they would be better. Then it is a matter of choosing either redundancy and word length versus potential conflicts with future borrowings and improper semantics.<br />
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An alternative would be to let the introducer be "''slerfa''-" (or something similar) for "selyle'u" and correcting the terminal "-u"; this might even lend itself to shorter words in some situations (by using "''sler(f)''-"). The bad news about this option is the fact that a word (and not just a rafsi-like fragment) called "slerfa" (or whatever) could