(02/19/2008, 12:24 PM)bo198214 Wrote: the bracketing must be to the right. So

ao(ao(aoa))=a+4

ao(aoa)=a+3

aoa=a+2

a = a+1 ???

The answer to that question comes clear if zeration is defined this way:

Neutral element:

This is similar to addition:

Neutral element:

Also is similar to product:

Neutral element:

And is similar to exponentiation

Neutral element: where I conjecture that "?" is the inverse function of tetration, and is not slog.

Note that the neutral elements are all related with the inverse of the higher ranked operation.

I think that it is a very important clue.

But why I choose as the neutral element of zeration?

-Because it is

-Because

-Because this sequence:

I conjecture that zeration has a periodic component, so it can just add 1 no matter how high are his variables, and also

ln(a+b) could be equal to ln(a) ° ln(b)

ln(a+b)=ln(a)+ln(1+b/a)

if a>b => 0 < ln(1+b/a) < ln(2)

If a=b => ln(1+b/a) < ln(2)

this is suspiciously like zeration, adding a small number to the larger number, or adding 2 if a=b