User blog comment:Chronolegends/Tetration on ordinals/@comment-1605058-20160524190634/@comment-24920136-20160524193529

I did find it strange that noone in this fine community hadnt published something of the sort

and, yep, this method can't work with succesor bases (ie. finite ordinals). I provided a way to relate tetration to exponentiation for natural numbers to themselves in a link, but i can't do that to ordinal exponents/heights.

To do so would require being able to use the binomial theorem on ordinals... (  λ + k )^x = undefined?

since for example it would imply stuff like  (   λ + k )^3 =  (   λ + k )*( ( λ^2)-( λ k)+(k^2)) and substraction is not defined for the ordinals.

therefore i don't think this  even    works for natural k and x, and much less for ordinal k and x. (but, like i stated, i might be wrong though i currently do not believe i am)