Beyond "^" ?

Question

Sometimes, one rule of arithmetic can be replaced with another one, and save time for both writer and reader. For example:

A + A + A + A + A... ["A" repeated A times] = A x A

A x A x A x A x A... ["A" repeated A times] = A ^ A

Now my question is:

A ^ A ^ A ^ A ^ A... ["A" repeated A times] = A [what goes here?] A

And whatever goes there, what do you write when that way of writing too is similarly exhausted, and what do you write when that too is exhausted, and so on, and so on?

Answer 1

This article may prove enlightening:

http://en.wikipedia.org/wiki/Graham's_number

Answer 2

You should read the book

" A world without time "

It compare Einstien and godel and the theorioes they came up with

Answer 3

A^(A^A), for many powers of a are taken.

Answer 4

hmmmmmmmmmmmmmmmmmmmmmm