numbers, counting and math

1. Cardinal numbers (One, two, three…)
   • Binary
   • Base 5
   • Octal
   • Base 24
   • Combined summary of cardinal numbers in all the bases
2. Ordinal numbers (First, second, third, fourth…)
3. Adverbial numbers (Once, twice, thrice, four times…)
4. Fractional numbers (1/2, 1/3, 5/7…)
5. Multiplitive numbers (Double, triple, quadruple…)
6. Distributive numbers (Two for each, three for each…)
7. Negative numbers (-1, - 234234…)
8. Special numbers (π, e, i…)
9. Basic math
10. Logic

Cardinal numbers (One, two, three…)

For historical reasons, several numeric bases is used in Taruven, namely binary, base 5, base 8 (octal) and base 24.

Few know or care about the binary system, which is mostly included here for completeness, though patterns of zeros and ones have a sort of pronounced shorthand that is used to describe binary patterns of all sorts, like for instance a chessboard. In the summary, this is the column for "colloquial binary".

Prior to the first grammar of Taruven, there were two competing systems in use; base 5 for everyday matters and base 24 for everything else. The empire later settled on base 8 for everyday matters, with a base 5 monetary system, and base 24 for science and engineering. In xāria, where as usual the Houses of course cannot use the same thing as the empire or a rival House, several different bases are in use for everyday matters, among them base 12 and 16.

Binary

aìle 0 þa 1

Names of patterns of zeros and ones

0: aìl
01: aìda
10: þaìl
11: þada
00: halaì
01: haìda
000: halelaì
001: halata
010: hatalaì
011: hatade
100: þalaìle
101: þaìleda
110: þadaìle
111: þatada

Base 5

These days, base 5 is used as the base for some forms of computing instead of binary, and for the lower denominations of the old monetary system. These days, the highest number possible in base 5 is 15624₁₀, that is 44444₅: kaìr-šīra kaìr-kanta kaìr-vynta kaìr-arta kaìr-kaìr.

Unique for base 5: nnta 5. nnta is used instead of the word for zero in compound numbers of base 5: 10₁₀ (2×5) is ran-nnta and not *ran-aìren.

0

aìren, aìle

1

þa

2

ran

3

hvenn

4

kaìr

5¹

nnta

5²

arta

5³

vynta

5⁴

kanta?

5⁵

šīra

Octal

Octal adds šu for 5, gaò for 6, di for 7 and hreì for 8. As with nnta for base 5, hreì is used for zero in compound octal numbers: 32₁₀ (4×8) is kaìr-hreì and not kaìr-aìren

0

aìren, aìle

1

þa

2

ran

3

hvenn

4

kaìr

5

šu

6

gaò

7

di

8¹

hreì

2×8¹

thallen

3×8¹

jaryan

4×8¹

kaìrre

5×8¹

šurre

6×8¹

gerre

7×8¹

dirre

8²

harran

8⁴

keryan

8⁸

raỳan

8¹²

leìan

8¹⁶

thuìlan

8³²

rišarga

The word for 16, thallen, is from the binary pattern 1000₂. The word for 24, jaryan, is likewise from the base 24 system. In some dialects, nnta from the base 5 system is used for 5 instead of šu.

Base 24

Base 24 adds hūš 9, myn 10, vru 11, allin 12, adren 13, arran 14, avryn 15, thallen 16, agrun 17, aỳra 18, ašora 19, ařan 20, avalle 21, atira 22, amara 23 and jaryan 24. While nnta and hreì is used for compound numbers like n×5 in base 5 and n×8 in octal respectively, jaryan is only used when the compound number is between 24 and 47, inclusive. If not, the much shorter yar is used instead: jaryan hreì 32₁₀ (24+8), but ran-yar hreì 56₁₀ (2×24+8). Furthermore, instead of *šu-yar the word šyar is used.

0

aìren, aìle

1

þa

2

ran

3

hvenn

4

kaìr

5

šu

6

gaò

7

di

8

hreì

9

hūš

10

myn

11

vru

12

allin

13

adren

14

arran

15

avryn

16

thallen

17

agrun

18

aỳra

19

ašora

20

ařan

21

avalle

22

atira

23

amara

24¹

jaryan

5×24¹

šyar

24²

utarha

24³

veraìn

24⁴

keìrye

24⁵

šinn

24⁶

gevan

24⁷

džaìn

24⁸

rahan

24²⁴

jarramān

Summary

Ordinal numbers (First, second, third, fourth…)

Number + =ax

1. kaìrax

   kaìrax
   kaìr -ax
   4    -th
   

   4th

Adverbial numbers (Once, twice, thrice, four times…)

In other languages, these are adverbs or adverbial expressions that tell how many times something is/was done. In Taruven this is done by a verbal suffix created by the ordinal prefixed with o-, as in example 1a) below.

2. 1. tšahohvenn

      tšahohvenn
      tšah o-    hvenn
      see  times 3
      

      I looked thrice
   2. tšahonn

      tšahonn
      tšah -onn
      see  many.times
      

      I looked many times

Fractional numbers (1/2, 1/3, 5/7…)

Fractions are constructed by prefixing vÿ(l)- to the denominator:

3. 1. kaìr vÿdi

      kaìr vÿdi
      kaìr vÿl- di
      4    FRC  6
      

      four sixths
   2. hvenn vÿlařan

      hvenn vÿlařan
      hvenn vÿl- aỳra
      3     FRC  18
      

      three eigthteenths
   3. vÿmyn

      vÿmyn
      vÿl- myn
      FRC  10
      

      one tenth
   4. hvenn vÿrišarga

      hvenn vÿrišarga
      hvenn vÿ- rišarga
      3     FRC 7.92×1028
      

      three 7.92×10^-28s

Named fractional numbers

jeì is also used for miniscule, smidgen.

Mixed fractions

hvenn a vÿdi 3 + 1/7

Multiplitive numbers (Double, triple, quadruple…)

Multiples are constructed by prefixing ō(g)-:

4. 1. ōran

      ōran
      ōg- ran
      MUL 2
      

      double, two times
   2. ōgařan

      ōgařan
      ōg- ařan
      MUL 20
      

      twenty times

It is quite likely that the multiplicative ōg- and the adverbial -o- derive from the same source.

Distributive numbers (Two for each, three for each…)

Distributive numbers are constructed by prefixing pe-, which simplifies to p in front of numbers starting with a:

5. 1. peran

      peran
      pe- ran
      DIST 2
      

      two each, by twos, two at a time
   2. pallin

      pallin
      pe- allin
      DIST 12
      

      twelve each, by twelves, twelve at a time

The distributive number prefix can be stacked with the fractional prefix.

6. pevÿran

   pevÿran
   pe-  vÿ  ran
   DIST FRC 2
   

   a half of each, by halves

Negative numbers (-1, -234234…)

Negative numbers are constructed by prefixing aì-:

7. 1. aìran

      aìran
      aì- ran
      NEG 2
      

      lacking two, minus two, two below zero
   2. aìaỳra

      aìaỳra
      aì- aỳra
      NEG 18
      

      lacking eighteen, minus eighteen, eighteen below zero

Special numbers (π, e, i…)

Basic math

x yhux = x^y

8. 1. nnta ranhux

      nnta ranhux
      nnta ran -hux
      5    2    …
      

      5₅², 25₁₀
   2. nnta ranhux þa

      nnta ranhux   þa
      nnta ran -hux þa
      5    2    …  1
      

      5₅² + 1, 26₁₀
   3. nnta te ran

      nnta te ran
      nnta te ran
      5    +  2
      

      5₅ + 2, 7₁₀
   4. nnta ōran

      nnta ōran
      nnta ō ran
      5    × 2
      

      5₅ × 2, 10₁₀
   5. šu vÿdi

      šu vÿdi
      šu vÿ- di
      5  ÷  6
      

      5₈ ÷ 6₈, 5₁₀/6₁₀

Logic

There's both a system of logic based similar to the western logic (binary, true-false) and one with five values. The former is well described elsewhere, and due to space-considerations the latter is left as an excercise to the reader :)