f( f(x) ) = exp(x) solved ! ! !

[bo198214]

1) i dont have math software and cannot make those graphs.

Sage is a free enormous powerful math software.

2) you probably do have the software to make those plots and since you get the idea, you could make those plots yourself.

Yes but its some effort, no math software has implemented half iterates via regular iteration.

that way your also certain that the data is not manipulated or carefully selected.

I think this is more an issue in other sciences not in mathematics.

3) the truth of math does not depend upon someones capability of making graphs. call me oldfashion.

The truth of math depends on nothing. However if you want to show that truth to someone, then you have to convince him. Usually this is done by giving a proof. If that can not be done, then other ways should be sought.

however i believe most here assume analytic tetration exists and is unique ?

Existence was shown by Kneser. Uniqueness is a mostly unresearched yet. Sure is that it is not unique by analyticity alone.