08/11/2009, 12:06 AM

So guys,

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

Roughly:

An -exponential is the times application of to .

An -logarithm returns the number of iterations of necessary to be applied on to obtain .

Additionally we may also have:

An -power is the times application of to (same as -exponential but function in , not in .)

Implicitely there is contained the concept of the Abel function: is an Abel function for each and that of a superfunction/iterational is a superfunction for each .

Also ability to specify an initial value 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" -exponential, while the prefix "super" rather suggests "the" superfunction, super-exponential.

" is an -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.)

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

Roughly:

An -exponential is the times application of to .

An -logarithm returns the number of iterations of necessary to be applied on to obtain .

Additionally we may also have:

An -power is the times application of to (same as -exponential but function in , not in .)

Implicitely there is contained the concept of the Abel function: is an Abel function for each and that of a superfunction/iterational is a superfunction for each .

Also ability to specify an initial value 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" -exponential, while the prefix "super" rather suggests "the" superfunction, super-exponential.

" is an -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.)