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:
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