Note that for all of this blog post ranges over the limit ordinals.

I don't provide a method for exponentiation nor tetration for succesor bases. in other words is not something i here provide a sequence for. (Nor do i think it is as trivial to do so at this moment, but i might be wrong!)

I begin with a reminder of how to reach

A.- for succesor exponents the sequence is , , ...where is the nth member in the fundamental sequence of

B.- for limit exponents the sequence is ,, ... where is the nth member in the fundamental sequence of

Note that A works even If is a fixed point such that ->

ε0 is related to tetration by the sequence ,, ... and can be represented as the uglier but still intuitive

i give instructions on how to express tetration as exponentiation for natural numbers here:

http://googology.wikia.com/wiki/User_blog:Chronolegends/Tetration_related_to_iterated_exponentiation

The above Works for natural numbers only, for ordinals substraction is not defined, so the instructions must be changed a bit, since for example

leads to an undefined result, because it involves ω-1

So the way works is this

A.- for ordinals with succesor "heights"

B.- for ordinals with limit "heights"

where is the nth member in the fundamental sequence of

A few Examples