TOKI  I O 

For accustomed of Toki pona, the difference in diction and the difference in significance of a continuation of figures are fundamental. These differences make operational the speech of the numbers in Toki IO.
In toki pona, the numbers known as are additions which should be carried out.
In Toki IO, the numbers are known ass they are written, and what is said, which is written, is exactly the value of the number. The names of the current numbers are memorized more easily than one believes in the first access.

o or O: zero, pronounced [ o ]
i or I: one, pronounced [i]

io signify "number" and it is pronounced [ io]

the numbers break up according to the position into powers of IO (2)   THE UNIT IS AT THE LEFT! It's the opposite of the classical binary system.

The addition i+o=i ; i+i=oi ; oi+i=ii

Thus OI is 2 decimal, the II three.

+ is pronounced "oto"
- is pronounced "no oto "

= is pronouncedt "iko"
 

Multiplication ixo=o ; ixi=i

x (to multiply) is pronounced "ito"

÷ (to divide) is pronounced "ko"

= is pronounced "iko"

a^y is pronounced : "[a] toti [y]"

Writing: the numbers are an indicating alignment of figures of the powers of 2.
To facilitate the reading and the pronunciation, an apostrophe separates the figures from two into two starting from the left.
This apostrophe corresponds to an installation of the voice, something like a musical sigh, but does not have a particular mathematical value. It is not absolutely necessary of one facility (quite useful moreover).

example : ii'oi'ii'oo'i

which one immediately sees with the beginning by I that it acts of an odd number.

You can break up this number all things considered of powers of 2

(1x1)+(1x2)+(0x4)+(1x8)+(1x16)+(1x32)+(0x64)+(0x128)+(1x256)= 315

Practical: the double of 315 will be obtained by adding an O with the left-hand side of the number
315 x 2 = 630

ii'oi'ii'oo'i x oi = oi'io'ii'io'oi

and half of ii'oi'ii'oo'i (an odd number) will be: i,io'ii'io'oi  (315/2=157.5)

Fractional numbers: One can use a comma (french system) or a point (like English) to
express a fractional number, as bases 10 of them. IO'O, IO'II

Pronunciation: the numbers are read in litany, by words of two digits starting from the left, by marking a light installation between two pairs of figures. Each pair is accentuated like a word, always the first syllable of the word.

Comparisons : The expressed numbers bases ten of them are more concise in general than those expressed bases two of them, in parallel one can also say that those expressed bases sixty of them are more concise than those expressed bases ten of them. But when one not considers the figures but their expression in letters, the things are not so clear.

That one judges some: 3254

• in Danish for example, a number as 3254 will be expressed while juggling between the bases ten and twenty; it states 3 thousand 2 hundred and 4 and half of the 3è time 20, is tretusindetohundredefireoghalvtreds
• romanical numbers: MMMCCLIV 
• décimal: 3254
• binanry : 110010110110
• toki io : oi'io'ii'oi'oo'ii

But in case of using letters, it may be some different!

toki io : oi'io'ii'oi'oo'ii> soit  12 lettres et 12 syllabes
french : trois-mille-deux-cent-cinquante-quatre >> 32 letters or 9 syllabes
danish :  tretusindetohundredefireoghalvtreds >> 35 letters or 12 syllabes
english : three thousands two hundreds fivety four > 35  letters or 10 syllabes
toki pona : (1257 fois 2) tu tu tu tu tu t u ........................tu tu tu tu  > 3254 letters or 1257 syllabes
(or then: MUTE MUTE MUTE >12 letters and 6 syllables, but without any precision.)

Toki IO accepts all the mathematical signs, like any language. The difficulty is to be able to name them. With regard to the letters of alphabets different from that of Toki IO (which has only six letters:
marked i, k, n,o,t,z: [ i ] [ ik ] [ in ] [ o ] [ it ] [ iz ]) one uses the transcription in International Phonetic Alphabet

example: "A" will be said [ a] and "µ" will be said [ my ].

Here some words:

iti: line in general >thus a curve;
iti tino: a stable line> a line
iti nizo: an ordered line> a vector
iti toti: a line squared> a plan
iti tino ko: a divided line >a half-line
iti toko: a broken line >a segment of right-line
iti toko toti: a segment of
line squared> a square
to iti: a point of a curve
to iti toti: a point of a plan
kono: an angle
ii ii kono: a triangle (* * ii kono: three angles)
io'oo ii kono: an octagone (* * * io'oo' ii kono: 35 angles)
siko:circle
siko siko: a sphere(?)
iti toko toti ii: a cube (* * *Caution! if a word must follow ii which is the exhibitor, it is necessary to use the particle "Ti" to prevent that "ii" is perceived like the indicator of a made up name.)

A>B :  [a] zoi [bi]

A<B :  [a] zoo [bi]

SET : tozo

Set with order : tozo tino oi ("set stable number")

Implication : toti  (Caution with the possible ambigüity with Toti used for saying "power")

A + B : [a] oto [bi]

A x B : [a] ito [bi]

non A : no [a]

A = B : [a] iko [bi]

A | B : [a] ono [bi]

A element of B (AB) : [a] to [bi]

A not element of B (AB): [a] no to [bi]

A inclused in B (A B): [a] zoni [bi]

A contains B (A B) : [a] ki kiti [bi]

The circle says ziko
the angle says kono
the sine says "snake numbers": ziti io
the tangent says "height numbers": kiko io
("Egyptian Al-Hasib, called "the Calculator", studied the properties of the tangent function at the end of IXe century. This is why Al-Hasib has of him even definite the tangent as being the ideal tool to measure heights." http://www.trigofacile.com/maths/trigo/notions/fonctions/tangente.htm )

NOTE :
the system of the numbers in Toki IO is usable in any language using an alphabet where letters I and O have about the form of the 1 and of the zero and correspond to vowels. It is true in English, French, Spanish... about all the languages using a Latin alphabet or Greek or Cyrillic. For the other languages, I do not know.
This system linking calculation, writing and diction of the number is practical for using a system at base two, therefore two chiffres.