changing terminology (was: overview paper co-author invitation)

[Base-Acid Tetration]

Actually, it is a prefix

no, -iter- is not a prefix, it's a word-stem of latin that means repeating.
but i have no problem adopting it as a prefix. it's clearer than "super".

So guys,

to solve our current problems, I come up with the following quite memorizable and hopefully non-confusing suggestion:

Roughly:
An \( f \)-exponential \( \eta_z(w)=v \) is the \( w \) times application of \( f \) to \( z \).
An \( f \)-logarithm \( \gamma_z(v)=w \) returns the number \( w \) of iterations of \( f \) necessary to be applied on \( z \) to obtain \( v \).
Additionally we may also have:
An \( f \)-power \( \varrho^w(z)=v \) is the \( w \) times application of \( f \) to \( z \) (same as \( f \)-exponential but function in \( z \), not in \( w \).)

Implicitely there is contained the concept of the Abel function: \( \gamma_z \) is an Abel function for each \( z \) and that of a superfunction/iterational \( \eta_z \) is a superfunction for each \( z \).

Also ability to specify an initial value \( z \) on which the iterations are applied, was often asked for here on the forum.

Another thing is that imho it lets one think more in the direction of "a" \( f \)-exponential, while the prefix "super" rather suggests "the" superfunction, super-exponential.
"\( g \) is an \( f \)-exponential". (How do the native speakers think about it?)

So we can leave the old super-notation in there previous meaning (though I think it is an unnecessary notation as everything can be specified with tetra-, penta-, etc. prefixes.)

it will be confusing w/ my greek prefix terminology (tetra-, etc.). is a tetra-exponential an iterate of tetration b[4]x, as your terminology would suggest, or is it an iteration of b^x?

but you don't need to worry about english, i thought you were a native speaker the first time i was here, i never knew you were henrik trappmann, a guy in germany