Recursive system of monary operations

Each class of monary operations may be designed as a recursive function of a previous order class of operation, but the subiphication operation may not have a previous order class of operation. Therefore, subiphication is taken here as a zero order arithmetic operation within the monary operations. Subification may be considered a percepcion of number in things. I'll may name subiphication as 0 order operation or no-operation considering that for it there is no number over which to operate, subiphication operates over things' dimensions and limits.

Notice that defining subiphication as a zero order mental operation on quantiphication can be put into question if we take into consideration that there are more rudimentary notions of quantity, particularly: many and few, more and less, these perceptions related to quantity may imply a fuzzy perception of number, and they may be put as some more elemental perceptions of quantity than and previous to subiphication, as subiphication is a clear perception of number already. Understanding this may help also to understand the following.

Lets follow with the subject of the recursive system of monary operations, for example, monary counting, which I'll name either countiphication or monophication (from arithmetic operation Nº1), it may be designed as subiphicating a subiphied number, it may be subiphied a number 2 out of 2 subiphications of I and I instead of subiphying 2 directly from:

II 

when both strokes are separated from each other by a relevant gap, each one may be subiphied in a distinct subiphication, becoming conscious of both subiphications joinly and combining them into a single amount is counting:

I    I

Which is counting I two times: .I.I

Thus having countiphied two from one by one, this does not imply that we may not design several types of countiphication, by one:

I    I    I    I... which is counting n times I.

As in .I.I.I.I which is counting 4 times I.

by two:

II    II    II... which is counting n times II (counting couplets or pairs)

As in .II.II.II which is counting 3 times II.

by three:

III    III    III... which is counting n times III  (counting triplets)

As in .III.III.III which is counting 3 times III. 

Numerical quantities bigger than triplets may be countiphied even think they may not be subiphied, this means that it is unlikely that a system of counting in tetraplets may be developed within the scope of a single countiphying (as 3 pairs is always 1 pairs... 2 pairs... 3 pairs, unless we multiply 3*2 nevertheless multiplying is beyond the scope of simple countiphying but it is within recursive countiphying. 

Notice that countiphying n times is not itself a number. As countiphying is done over a number, think the most often we count one by one, we may count by pairs, by tens, by docens, etcetera. Countiphying n times is just a first order operation.

A monary addition type of operation, which I'll name addiphication, or biphication (from arithmetic operation Nº2), may be designed from the simplest form of countiphication, as countiphying an already countiphied number. For example:

+2 = +I.I.

as in:  5 =  3 +2 = I.I.I. +I.I.

Adiphying 2, where 2 comes from countiphying II, is: countiphying (countiphying II), then in adiphying 2 is nested a countiphication of II.

A monary multiplication type of operation, which I'll name Multipliphication, or triphication, (from arithmetic operation Nº3), may be designed from the simplest form of the addition -biphication-, as adding again an already added number; or as follow counting with the already counted countiphication. For example:

n*2  =  +n +n = I n times and I n times

n*3 = +n +n +n = I n times and I n times and I n times

as in: 3*2 = +3 + 3 = I.I.I. I.I.I. = 6

It may noticed that *2 does no represent a number, because *2 is the number of times that n, or 3 in the example is biphicated, so *2 represents an operation, whilst 3 is a number over which the operation is realized. 

A monary exponential type of operation, which I'll name tetraphication (from arithmetic operation Nº4), may be designed from the simplest form of the multipliphication -triphication-, as multiplying an already multiplied number; or as adding an already added addition; or as counting an already counted countiphication of a countiphication.

n^2 = n*n = +n n times  =  n times conjuction of I n times

as in: 3 ^2 = *3*3 = +3 +3 +3 = I.I.I. I.I.I. I.I.I.

It may be noticed that ^2 is not a number, it is an operation (as ^2 represents the number of times that 3 is *3.  Whilst 3 is a number over which a operation is realized.

There is a series of monary operations, to the arithmetic operation Nº4, it may follow, a Nº5, a Nº6, a Nº7 and more operations. That is, to subiphication, addiphication, triphication　and tetraphication it may follow a pentaphication, a hexaphication, a heptaphication, a octophication, and more operations. 

By a number it may be understood here an element of a numeric system, within a number some operations may be implicit and some operations may be implicated, but in a number neither there is an operation explicit nor an operation explicated. For example: 25 where we understand 2*10 + 5, and we may analize count II as many times as counts of I in IIIIIIIIII and to it add the result of counting IIIII. So, by this definition 25 is a number because it is an element of the numeric system with base 10. 20+5 is not a number, because the operation +5 is being expressed on it; and +5 is not a number, but the expression of an operation.