New terminological standard for superfunctions.

[tommy1729]

yeah but it does not matter if we solve 

f(2x) = exp(f(x))

or 

g(x+1) = exp(g(x))

essentially those equations are equivalent.
And even though they might not hold everywhere , where they do also transfers when you change one into the other.

Instead of using new names, just write out the equations explicitly.

...

Again, Tommy. I think you misunderstand the point.

What do we call a map, such that,

\(
f(F(z)) = G(f(z))\\
\)

If we are in a space where, inversion (and hence, conjugation) doesn't make sense.

This is just to agree upon terminology. Mphlee is working on the categorical aspect, and he's wondering if there's a good word; or trying to find an agreed upon word.

This is incredibly relevant to this forum, because it's the principle of the base change function; but we're not necessarily assuming invertability.

Yeah I misunderstand the point or I miss the point assuming there is one.

You talk about space and inversion.

What space ??

What inversion ??

I can define the exponential function for square matrices , real numbers , complex numbers and a few other numbers.
In general use taylor series.

But for nonassociative numbers or things that are not numbers I have no idea how to define them.

I can not define exp(x) when x is a space , operator , set , ... 
I only know exp(x) when x is a ( traditional type ) number ( including a finite set like mod p or a cardinal number )

And what about inversion ?
Set inversion ? group inversion ? functional inversion ? multiplicative inversion ?  
And since we are apparantly not talking about complex numbers or riemann surfaces , what do you mean by conjugation ?

So before I replied I started reading about " space " and exp but I was not able to find a definition for exp of a " general " or " nontrivial " space.

And do we even still have exp(-x) = 1/exp(x) since we apparantly "lost" inversion ??
So we also lost substraction ?

And how is all this space thing important for tetration and base change anyway ?

Btw I thought we were here to find (complex-)analytic tetration , so why go into non-analytic subjects and then call them crucial ??

Sorry to ask.

regards

tommy1729