Numbers (TI/j-)

Numbers are important to communicate and serve many purposes. Eberban numbers are expressed as a chain of TI particles (any particles starting with t-), which can optionally contain separators and a terminator starting with j- to make more advanced numbers.

Digits

Numbers are mainly composed of digits (TI family), which are chained one after the other, starting from the highest significant one to the lowest, and is by default expressed in base ten.

te ta thus means 12 while tei ti tu means 904.

While it is normally not allowed to use a digit higher than the base, it is allowed if only one digit is used since there is no ambiguity over its value. teo is thus B/11, while teo ti is not allowed in base ten.

The series described in the table is infinite and can be expanded if the speaker wants to use larger bases by iterating over the vowels in order and skipping cases where the same vowel appears multiple times in a row (since Eberban considers multiple identical letters the same as a single one)

ti, ta, …, tu
tie, tia, …, tua, tuo
tiei, tiea, …, tuoa, tuou

Number syntax

Numbers follow the following syntax with some parts being optional:

base ju integer-part jo fractional-part ja repeated-part je magnitude

1. Optionaly the base of the number can be expressed by a single TI followed by ju. This TI is the last digit of the base used, thus tei ju is base ten, teo ju is base twelve, and tao ju is hexadecimal. If absent it defaults to base ten (tei ju), unless the default base is overwritten in the context (TODO: Add word to set such default base).
2. The integer part of the number, as a string of zero or more digits TI. If there are zero digits then a fractional part is mandatory, unless je is used.
3. This integer part can then optionally be followed by jo and a fractional part which is also a string of zero or more digits TI. joi can be used instead to also make the number negative.
4. If there is a fractional part, it can be followed by ja and a repeated part which is also a string of at least one digit TI. The number has these digits repeated indefinitely.
5. Regardless of the presence of a fractional part or integer part, the number can then contain je followed by a magnitude, which is a string of at least one digit TI. The value expressed is the previous part multiplied by \(\text{base}^{\text{magnitude}}\). jei can be used instead to express a negative magnitude. If only the magnitude is present then the integer part is considered to be equal 1.

Examples :

• teo ju tie tia = \(56_{12}\)
• tu ta = \(42\)
• to jo te tu te tie tei = \(3.14159\)
• to jo te ja to = \(3.1\overline{3}\), \(3.1333\dots\)
• to jo ja to = \(3.\overline{3}\), \(3.333\dots\)
• to joi = \(-3\)
• tia jo ti ta ta je ta to = \(6.022 \times 10^{23}\)
• tei jo te ti tei jei to te = \(9.109 \times 10^{-31}\)

Various usage of numbers

Numbers have various usages which require different definitions and arguments. The desired definition can be selected by ending the number with a particle of family JI (jie is inferred if omitted). jie is mandatory between consecutive numbers to tell them apart. Particles other than jie must follow positive integer (no fractional part).

• ji: [E:tce* a] is (a group of) [number] things satisfying [A:(tca a)].
  Speaks about a set of expressed cardinality.
• jia: [E:tce* a] is (a group of) [number] things satisfying [A:(a)].
  Same but uses the raw property variant of set definitions.
• jio: [E:tcu a] is (a group of) the only [number] things satisfying [A:(tca a)].
  These are the only things that satisfy the property. There is nothing that satisfies A which is not in the set.
• jioa: [E:tcu a] is (a group of) the only [number] things satisfying [A:(a)].
  Same but uses the raw property variant of set definitions.
• jiu: [E:tca a] is the [number]th member of sequence [A:blu a].
  Speaks about an element in an ordered list. Index follows zero-based numbering, such that the first element is the 0th.
• jie: [E:tce gan] is the number [number] times [A:tce gan] (default: 1 unitless).
gan is the word for a number, and both arguments are sets of numbers. These sets allow handling many numbers (ranges, approximations, or even arbitrarily constructed ones), and math operations are also defined using sets to distributively operate on each value of the set. The A argument allows multiplying this number with another number such as unit numbers (“1 meter”, “1 kilogram”, etc). The A argument defaults to 1 unitless.

Note that the raw property of set definitions refers to the fact that sets have two types of predicates: one where a member must satisfy argument (a) and the other (tca a). Many predicates expect their arguments to be sets, so the latter is usually used. The former allows accessing raw members, an example use case is dealing with nested sets.