01/08/2008, 08:52 AM
andydude Wrote:Ivars Wrote:both finite and infinite, and its opposite log(log(log(log(log(.....) both finite and infinite?What?
Oh, I get it now. You are mistaken, \( \log^n(x) = {}^{\text{slog}(x)-n}e \) which is not the inverse of tetration... it is tetration.
Tetration has two inverses, super-roots and super-logarithms. You might be able to consider super-logarithms as iterated logarithms, but instead of giving the nth iterate of a logarithm, the super-logarithm gives you the n required to produce the given iterate. Please see Wikipedia's super-logarithm and iterated logarithm for more.
Andrew Robbins