# Lwaitel numbers

## Forming the numbers

Lwaitel uses a base 6 number system, with the following digits:

English digitLwaitel digitName of digitSign
00un
11í
22na
33pal 
44pin 
55

When writing numbers as numbers, digits are written with the largest place value first as in English.

To construct words for larger numbers up to 36, just put two digits together; e.g., í un = 106 = 610; pal pin = 346 = 2210. (I'm using subscript 6 here to indicate that a number is in base 6.) In speech, when this causes two vowels to be next to each other, the vowels become a diphthong (e.g., í un is pronounced iun ). When signing, use your dominant hand for the ones place, and your non-dominant hand for the sixes place, and put the hand showing the sixes place above the hand showing the ones place. For numbers 36 and larger, each group of two digits is separated by one of the following words:

ValueWord
36 (62)lya 
1296 (64)níli 2
46656 (66)páli 3
1,679,616 (68)pínli 4
60,466,176 (610)lúli 5
2,176,782,336 (612)lyáli 

To sign these words, sign the word for 1, 2, 3, etc. with your dominant hand and put the index finger of your non-dominant hand horizontally in front of the sign (or all fingers for lyali). For instance, 1236 would be written í lya na pal (1 36 2 3), and 123456 would be written í níli na pal lya pin lú (1 1296 2 3 36 4 5). Groups of digits at the end containing only zeroes are usually omitted; a digit zero at the beginning of a group (other than the first) can be omitted, but usually isn't for numbers larger than four digits. An initial 1, however, can't be omitted (36 is í lya, not just lya).

The words lya, níli, etc. may be written inside a number written as a number; in that case, níli and above usually have their first syllable abbreviated with a digit, which is written in green, underlined, and the underline connected to the li (e.g., 2_l = níli). (FIXME this won't work if you have "print" selected instead of "cursive".)

### Non-natural numbers

únli 0 is a decimal point. mip  separates a numerator from a denominator in a fraction; if the numerator is 1, the numerator can be omitted. aunchent  precedes a negative number; if the number is written as digits, X is used.

### Automatic converter

Type a number in one of these boxes to see how it's said and written in Lwaitel.

Base 10:

Base 6:

Written number:

Written number (with separators):

As words:

## Prefixes for numbers

In a sentence, numbers are usually prefixed with a particle indicating how the number is used. This particle can contract with the next word following the same rule as for prepositions. When a number is written as digits, it's often written in a color showing which particle is used instead of the particle itself being written; when it's signed, however, the particle is still used (and not contracted with í).

ParticleColorMeaning
he BlackCardinal number (used to show how many of something there is)
u BlueOrdinal number (used to talk about a specific number in a sequence)
hau RedNumber used as a noun (for instance, when talking about math problems)
mip GreenFraction (used as a noun or cardinal)
ish GreenFraction of a group
(empty)BlackUsed with measurement terms (the measurement term precedes the number, though)
lwe ha  (Red)Used for items assigned a specific number (e.g., room numbers)

The prefix he is not used when signing. To indicate ordinals in sign language, wiggle the last finger of each hand for the first group of digits (last = whichever wouldn't be there if the number were one digit lower).

When a number is negative, aunchent goes after the particle.

Ordinal numbers start with 1. Aunchent (X) can be used with an ordinal number to indicate that one is counting from the end; in that case, the last item is zero (due to the other meaning of aunchent, "except": last except for one would be the second-to-last). If one is talking about the last item rather than the second-to-last, one would use ípu instead.

Ish is used for fractions of a group of countable objects, whereas míp is used for fractions of other things and for fractions used in math. he x míp x, where x is the same both times, can be used to mean that a thing has been divided or cut into x pieces.

## Approximate numbers

One of the words that can separate parts of a number can be used without any prefixes or digits to indicate an order of magnitude, similar to use in English of words like hundreds, thousands, millions, etc. (e.g., in "There are millions of words in the English language").

For other approximate numbers, nel "like" can mean "about", "around", and ngím "between" can separate two ends of a range.

## Math

Mathematical operations are expressed as follows:

• Addition: the conjunction se ("and") is placed between the two numbers. Both numbers still have their particles.
• Subtraction: the preposition aunchent  ("except") is placed between the two numbers. This can be written as X. The second number gets the same particle as the first. If the number is a cardinal number, the prepositional phrase goes at the end of the noun phrase.
• Multiplication: the numbers are written next to each other, and all but the last get the particle he (the last number gets a particle depending on its use).
• Division: the word mip  is placed between the numbers, and the second one doesn't get a particle.
• Exponent: the exponent comes first and gets the particle u.

Whole words can be used as variables. The words an, al, and im are used as generic variables (like x, y, and z).