05/15/2021, 11:57 PM
(05/15/2021, 11:25 PM)tommy1729 Wrote: It was established some years ago that other branches of tetration satisfy being the super of ln(x) + 2pi i or exp(x) + 2 pi i and similar results.
I believe Sheldon was first.
Is there any other thing about this branch hype of Leo that I missed ?
Not trying to be mean, but not sure why so much interest in it.
I mean it is either rather not interesting or not new as far as I can see.
It is just riemann surfaces ??
I do welcome and respect this new member though.
He clearly has insights and belongs here , no mistake.
Welcome Leo
regards
tommy1729
Hey, Tommy.
Different branches of tetration certainly do not do what you are saying. There are uncountably many solutions to the tetration equation; so I don't know what you mean by this.
This has to do with designing a classification of conjugate functions (or rather, we're trying to figure out what to call them first). Then we're trying to classify them. Or at least study their structure; in which we can consider them algebraically.
It's a very rich field, which is more in tune with abstract algebra; but you can do very quick manipulations if you have the set \( \[f,g\] \) be well defined. Such as modding out by this to form an equivalence relation; and then treating all elements in this set as one thing. But in order to do that, you need to understand the structure of it. And in what space it sits in which you can mod out. AT least, that's what I find so interesting about it. Mphlee is definitely more interested in the category aspect; where this relates very nicely to category theory.
Oh, Mphlee. I guess I misunderstood what equivariant means. I think this is the perfect term. I'll cast my vote for that. I thought it was reserved for,
\(
\chi(f(t,x)) = f(t,\chi(x))\\
\)
I didn't realize it could be null in the t variable.