Number system

The Qohenje number system has no "base" in the same sense that the Arabic system is base-10, binary is base-2 etc. Qohenje numbers have a fractal base system which can be expressed as base 4x+1...

The Qohenje numbers are constructed on the basis of the fundamental dimesions of reality:

a point (unity, 1)		a line (duality, 2)
a plane (defined by three points, hence 3)		space (defined by four points, 4)

The peculiarity of the system is that its "base" is defined by a fifth condition, that being the unity of the fourth condition, considered separately from the four points that define it. The first "decimal" slot (after the "ones") slot is hence 5. The base system can be thought of as the fractal repetition of this prismic structure, with each vertice becoming a new prism ,

This structure - the next "decimal" slot - has four unified prisms, each representing "5", for a total of 20, plus its own unity, making a value of "21". The next "decimal" slot after the 5s is therefore the 21s, followed by the 85s and so on.

Digits

The system has just six digits:

0 ( )

1 ( )

2 ( )

3 ( )

4 ( )

(3x+1) ( )

Numbers are built with the smallest slot on the left (the reverse of the Arabic system).

The digits , , and show the multiplication value of the slot in which they occur (just like for Arabic numbers). The digit ( ) however, does not occur in compound numbers. It stands exclusively for "4" and does not occur elsewhere.

( ) represents three times its slot value plus one (3x+1), hence,

(3*1+1)+(2*5) = 14

(3*1+1)+(3*5) = 19

(3*1+1)+(3*5+1) = 20

The existence of is mandated by the non-whole-number nature of the base. Note that has limited distribution: the appearance of a in any slot implies the appearance of nothing but to its left. So, although the number 16 could logically be written

  

(i.e. (0*1)+(3*5+1)), in fact this violates the distribution of . The number 16 can hence only be written,

  (i.e. (1*1)+(3*5)).

Counting

(Note that when enumerating countable objects, the partitive must be employed.)

Major decimals

"Countdown numbers"

The so-called "countdown numbers" (those containing a ) take up the multiplicative slack casued by the non-whole number base. There will be as many countdown forms as there are decimal slots in the next number form without . The major countdown lexical forms, along with their associated numeric sequences are given below :

Note that, because of the distributional rule for , the above forms show only the rightmost . These countdown forms will either have nothing to the left, or else an unbroken chain of , but cannot have any other digits.

To the right, there will be an unbroken chain of as many as are indicated in the chart, before either the end of the numeric form, or else a different digit (not ).

The digit sequence shown above hence uniquely identifies the countdown form indicated, with the largest possible form being the appropriate choice. Note that these countdown forms do not correspond to specific numbers. There will be at least one such form before each new multiplication value in each slot (see the example counting numbers from 1 to 100 above for examples).