Approaches to Tetration

[bo198214]

Hmm - I'm focusing different paradigms here; the goal to extend the operator hierarchy is not always driven by a functional representation. One may call it a "naive" approach - but this sounds somehow pejorative in some ears. Anyway - there is a strong effort to extend the (binary) operator hierarchy solely based on the properties of the usual operators.

I dont know what you mean. The only ways I know of to extend tetration is via series and limits. What binary operator properties lead to a definition of tetration?