10/01/2007, 07:32 PM

bo198214 Wrote:... then we have a more serious problem.

If you define to be different from 1, say , then . And in common use of the word tetration (hopefully you dont want to change this for the sake of continuity of your construction).

So if you accept this then any (real) value of different from 1 poses the contradiction . You see that it is necessary to define .

I see your point. My definition forces:

...

which, I guess goes against standard notation. I am leaving for vacations tomorrow, so I will try to examine the function defined as above and see if there's anything more interesting about it. If there is, I will report it back in a week or so.

Thanks to all who participated.