09/08/2009, 01:20 PM
(This post was last modified: 09/08/2009, 01:36 PM by Base-Acid Tetration.)
Quote:No, haha, it doesnt cheat. An entire function takes on every value infinitely often. Particularly the value 0, say sexp0(z_0)=0. Then you can just shift the function letting sexp(z)=sexp0(z0+1+z), then sexp(-1)=0. And by the equation sexp(z+1)=exp(sexp(z)) you get real values on all integers > -2.
i used the word entire to destinguish that tetration from the real ordinary tetration.
i thought entire meant holomorphic everywhere. if the entire tetration is with real values at integers, it can't be differentiable at z=-2