The Xaîni Counting System
The Xaîni numerical system is an octal system, which is to say it uses 8 as the base rather than 10 as in most human systems. This is clearly due to the fact that Xaîni have four digits on each hand, two fingers and a thumb on each side of them. The names of the numbers 1 to 8 are also the names of the thumbs and fingers, e.g.
| 1 | le | outer right thumb |
| 2 | kva | outer right finger |
| 3 | mir | inner right finger |
| 4 | pir | inner right thumb |
| 5 | yu | inner left thumb |
| 6 | kent | inner left finger |
| 7 | ner | outer left finger |
| 8 | lenner | outer left thumb |
The terms neichen and beichen, meaning the numbers 1 to 4 and the numbers 5 to 8 respectively are also in use, and also mean right hand and left hand.
These numbers are written in a symbolic notation which places its most significant digit on the right, i.e. exactly the other way around to our numbering notation, and which employs the zero (called ao, or aota, signifying emptiness).
The numbers from 9 to 16 are as follows:
| 9 | nasi le (nasi means something like other, different) |
| 10 | nasi kva |
| 11 | nasi mir |
| 12 | nasi pir |
| 13 | nasi yu |
| 14 | nasi kent |
| 15 | nasi ner |
| 16 | kavas |
The multiples of eight are:
| 16 | kavas |
| 24 | mirvas |
| 32 | pirvas |
| 40 | yuvas |
| 48 | kenvas |
| 56 | nervas |
| 64 | lenneravas |
and the intermediate numbers are formed in the same way as the numbers from 9 to 16, i.e. kavas le, kavas kva, kavas mir, etc. Similarly 65 is lenneravas le, and 90 (64+24+2) is lenneravas mirvas kva, and so on. The multiples of 64 (equivalent to hundreds in our system) are:
| 64 | lenneravas |
| 128 | karavas |
| 192 | miravas |
| 256 | piravas |
| 320 | yuravas |
| 384 | kendavas |
| 448 | neravas |
and then:
| 512 | mirtok (or 'mireri lenner', meaning the third power of eight) |
| 1024 | kva mirtok |
| 1536 | mir mirtok . . . |
| 4096 | pirtok (or pireri lenner) |
| 32768 | yutok (or yuveri lenner) |
All higher multiples use the powers of eight notation, thus:
| 262144 | kenderi lenner (sixth power of eight) |
| 2,097,152 | nerieri lenner (seventh power of eight) |
| 16,777,216 | lennereri lenner (eighth power of eight) |
| 134,217,728 | nasilieri lenner (ninth power of eight) |
and so on. This notation can be extended indefinitely, so that kenderieri lenner is eight to the power of 262144 and kenderierieri lenner is eight to the power of eight to the power of 262144. In compound numbers the 'lenner' part of the term is dropped to avoid confusion, viz.
270939 (262144+2x4096+512+64+24+3) is kenderi kva pirtok mirtok lenneravas mirvas mir
A highly specialised notation and naming system is used by Xaîni mathematicians for topology, imaginary numbers, and other aspects of higher mathematics, but I am insufficiently familiar with it to give you details.
Fractions use an octesimal system, except for half and one-and-a-half, for which the special suffixes -kantha and -kelantha respectively are added to the noun. Fractions are described in speech using the particle bein
bein (or bein le) one-eighth
bein kva two-eighths
bein mir three-eighths
bein pir four-eighths (half)
and so on.
Just as an English speaker might describe a long decimal, say 0.325184, as "point three two five one eight four", so the octesimal 0.325134 would be described in xathmel as "bein mir kva yu le mir pir".
Grammatically, the roots for numbers occur in all three grammars, and may be used in all three, although any mathematical discussion requires use of the middle grammar, which is always used for technical subjects. Numbers precede the noun in normal speech, and the noun remains in its singular form.