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

[tommy1729]

Actually I dont know whether it works, and I dont even have a hint, because there are no pictures provided. So if you can not prove it, why not convince us with some graphs of your approximation functions that show them converging?

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

2) you probably do have the software to make those plots and since you get the idea, you could make those plots yourself.
that way your also certain that the data is not manipulated or carefully selected.

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

4) i admit more research is neccessary and also proofs of uniqueness and existance.

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

5) i believe a lot is clarified if we can prove f_n(x) does not intersect with f_m(x) for any integer n and m and x > 1.

a graph might show if it does or not.

6) yes , im stubborn , dont use capitals at the beginning of a senteance and i make spelling mistakes

regards

tommy1729