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Sezimal Number System • Base Six Number System

Sezimal is a base six number notation and nomenclature;

Others may refer to sezimal base as sextal, heximal, seximal, senary, or simply base six;

You can see how sezimal works by using the Sezimal Calculator.

Sezimal groups digits in the traditional way of three‐digits grouping, naming each power of six accordingly:

0 zero10 six20 dozen30 thirsy
1 one11 seven21 dozen-one... ...
2 two12 eight22 dozen-two40 foursy
3 three13 nine23 dozen-three... ...
4 four14 ten24 dozen-four50 fifsy
5 five15 eleven25 dozen-five... ...

For 10² we use the numeral nif, from the Ndom word for «thirty-six»; up until here, it’s the same system proposed by jan Misali;

For 10³, we use the numeral arda, from the Sanskrit word अर्ध ‹ardha› /ˈɐɾ.d̪ʱɐ/ for «half» (of six), pronounced roughly as AHR-duh in English; we separate ardas from nifs with the “arda separator”, a narrow non-break space:

100 nif1󱹭000 arda10󱹭000 six arda100󱹭000 nif arda
200 two nif2󱹭000 two arda20󱹭000 dozen arda200󱹭000 two nif arda
300 three nif3󱹭000 three arda30󱹭000 thirsy arda300󱹭000 three nif arda
400 four nif4󱹭000 four arda40󱹭000 foursy arda400󱹭000 four nif arda
500 five nif5󱹭000 five arda50󱹭000 fifsy arda500󱹭000 five nif arda

For 10¹⁰, we use the numeral shadara, from the Sanskrit word षडर ‹ṣaḍara› /‍ʂɐ'ɖɐ.ɾɐ‍/ for (a wheel that has) «six spokes» (forming a hexagonal shape inside a circle), pronounced like shuh-DAH-ruh; we separate shadaras from nif ardas with a “shadara separator”:

1󱹬000󱹭000 shadara10󱹬000󱹭000 six sh.100󱹬000󱹭000 nif sh.
2󱹬000󱹭000 two sh.20󱹬000󱹭000 dozen sh.200󱹬000󱹭000 two nif sh.
3󱹬000󱹭000 three sh.30󱹬000󱹭000 thirsy sh.300󱹬000󱹭000 three nif sh.
4󱹬000󱹭000 four sh.40󱹬000󱹭000 foursy sh.400󱹬000󱹭000 four nif sh.
5󱹬000󱹭000 five sh.50󱹬000󱹭000 fifsy sh.500󱹬000󱹭000 five nif sh.

The shadara separator, when followed exclusively by zeroes, may function as an abbreviation for the six zeroes:

1󱹭000󱹬 arda sh.10󱹭000󱹬 six arda sh.100󱹭000󱹬 nif arda sh.
2󱹭000󱹬 two arda sh.20󱹭000󱹬 dozen arda sh.200󱹭000󱹬 two nif arda sh.
3󱹭000󱹬 three arda sh.30󱹭000󱹬 thirsy arda sh.300󱹭000󱹬 three nif arda sh.
4󱹭000󱹬 four arda sh.40󱹭000󱹬 foursy arda sh.400󱹭000󱹬 four nif arda sh.
5󱹭000󱹬 five arda sh.50󱹭000󱹬 five arda sh.500󱹭000󱹬 five nif arda sh.

The powers 10²⁰, 10³⁰ etc. form their names using Shastadari Prefixes, assuming the “sha” in shadara is a prefix for the sixth power:

10²⁰1󱹬000󱹭000󱹬000󱹭000dishadara
10³⁰1󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000trishadara
10⁴⁰1󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000charshadara
10⁵⁰1󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000panshadara
10¹⁰⁰1󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000nidara
10¹¹⁰1󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000nishadara
10¹²⁰1󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000󱹬000󱹭000nidishadara

To separate the integer part from the fractional/sezimal part of a number, we use the sezimal separator 󱹮 ― a vertical, thin wedge, point upwards, going up from the lowest position of the font’s descenders, up to the middle of the font’s x‐height, called simply “wedge”:

1󱹬234󱹭501󱹮105󱹭432󱹬1

arda and shadara separators are used both
to the left and the right of the sezimal separator

(one) shadara, two nif thirsy four arda, five nif one wedge one zero five, four three two, one

If you don’t have access to those separators, use the same ones your language/country already uses:

1,234,501.105 432 1
1 234 501.105 432 1
1.234.501,105 432 1
1 234 501,105 432 1

Finally, whenever we find needed or useful to indicate recurring digits on the fraction part of a number, we use the following recurring digit notation:

0󱹯1 / 0‥1 / 0„1 = 0.111… = 0.1̅ = 1⁄5 (zero and repeats one)
0󱹯05 / 0‥05 / 0„05 = 0.050505… = 0.0̅5̅ = 1⁄11 (zero and repeats zero five)
0󱹮0󱹯3 / 0.0‥3 / 0,0„3 = 0.0333… = 0.03̅ = 1⁄14 (zero wedge zero and repeats three)
0󱹮003󱹯50… / 0.003‥50… / 0,003„50… = 0.0035̅0̅ = 1⁄132 (zero wedge zero zero three and repeats five zero)

So, by writing the fractional separator twice, we indicate that what comes to the right of it repeats indefinitely; if the recurring part ends with at least one significant zero, we lock those significant zeroes at the right with an ellipsis.

 

Why sezimal?

With decimal: https://en.wiktionary.org/wiki/decem#Latin

Most descendant languages have changed the /k/ into an /s/ (French writes ‹x› but it’s not pronounced /ks/ or /k/).

The orthographic ‹c› or ‹z› in most languages is pronounced /s/, sometimes /z/ or /tʃ/.

So, /de.kem/ > /de.sem/ > /des/ + imal = decimal /de.si.mal/ (it kept the /s/ pronunciation because it originally was not an /s/, but a /k/, the ‹c› in the orthographies indicates just that).

For six what happens is: https://en.wiktionary.org/wiki/sex#Latin

No language descendant from Latin has kept the /ks/ pronunciation for the number (again, French writes ‹x› but it’s not pronounced /ks/).

They either have open syllables (ending an a vowel or diphthong), or have an /s/ coda; an /s/ intervocalic, in most romance languages, is vocalized into a /z/.

So, /seks/ > /ses/ > /ses/ + imal > /se.zi.mal/ ‹sezimal› (it was originally an /ks/, the /k/ dropped, and the /s/ vocalized to /z/ between vowels).