# BPFK Section: Mathematical Constants

This page is imported from version 18 of the page BPFK Section: Mathematical Constants from the lojban Tiki.

### cmavo xo (PA5)

#### Proposed Definition

Number question. A question word to which the answer is a number.

• {ma}

• what number?
• how many?

#### Usage Examples

xo gerku cu xabju lo zdani be do
How many dogs live in your house?

### cmavo ci'i (PA5)

#### Proposed Definition

Infinity. When followed by a number, it denotes a transfinite cardinal, such as ℵ0.

• {cimni}

• infinity

#### Usage Examples

ci'i da mulna'usle
There are infinitely many prime numbers.

#### Issues

As multiplication and exponentiation of transfinite ordinals is incompatible with that of cardinals, a new cmavo should be added for a transfinite ordinal, such as ω0.

### cmavo ka'o (PA5)

#### Proposed Definition

i, imaginary unit. When followed by a real number, multiplies that number by i. If four real numbers are separated by three ka'o, the number is a quaternion, with the components in the order 1, i, j, k.

#### Proposed Keywords

• imaginary number
• imaginary i

#### Usage Examples

saclu fi'ure loi lujna'u li paka'opa .iku'i saclu piro loi lujna'u li ni'upaka'opa
Only half the complex numbers can be represented in base 1+i, but all complex numbers can be represented in base i-1.

### cmavo pai (PA5)

#### Proposed Definition

The mathematical constant Pi (π), the ratio of a circle's circumference to its diameter.

• {te'o}

• pi
• π

#### Usage Examples

li pai du li ji'i ci pi pa vo pa xa
Pi is approximately equal to 3.1416.

### cmavo te'o (PA5)

#### Proposed Definition

e (ℯ), Euler's number

• {pai}

#### Proposed Keywords

• Euler's number
• mathematical constant

#### Usage Examples

li te'o te'a ka'o bi'e pi'i pai su'i pa du li no
'ei *𝜋+1=0

### cmavo tu'o (PA5)

#### Proposed Definition

Null operand. A placeholder digit used in MEX operations that are grammatically binary, but semantically unary.

• {zi'o}

#### Proposed Keywords

• null operand
• placeholder digit

#### Usage Examples

li fu'a ciboi muboi vu'u du li fu'a reboi tu'o va'a
3 5 - in reverse polish notation equals the negative of 2