Re: Why is the tetration so much harder to extend than the factorial?

On Mar 2, 10:58 pm, Mariano Suárez-Alvarez
<mariano.suarezalva...@xxxxxxxxx> wrote:
On Mar 2, 8:05 am, mike3 <mike4...@xxxxxxxxx> wrote:

On Mar 1, 4:41 am, "G. A. Edgar" <ed...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:

I think you are correct.

Well it's the only answer that would make sense to me. It then raises
the question of why are so many interesting statements about tetration
so difficult to prove/disprove (such as the derivatives-having-no-
zeros
"uniqueness" hypothesis for bases in (1, e^(1/e)].)?

Since you do not even know such a thing as tetration
even exists, it is not surprising that minor details
such as uniqueness, and derivatives avoiding some
values are elusive...


What do you mean by whether or not tetration "exists" or
not, anyway? One can come up with plenty of functions that
solve the two main functional equations, the only question is
which of those functions do we use as a suitable extension
to real/complex numbers, like the problem with the gamma
function providing a suitable extension of factorial.




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