08/11/2009, 08:38 AM

(08/11/2009, 02:17 AM)andydude Wrote: I have also heard of the "infra-logarithm" which would be the only conflict with this approach.

(08/11/2009, 02:37 AM)Tetratophile Wrote: ps. then the tetra-logarithm would be infra-exponential, not infra-logarithm.

Ultra and Infra are made from observations of growth.

Ultraexponential grows faster than the exponential

Infralogarithm grows slower than the logarithm.

Thatswhy Infra-F is not the Abel function but the Abel function of the inverse of F. (which is theoretically not really useful)

In the same way "super" is a pretty memorable concept (bigger, grows faster) if it was not already used for super-logarithm. Which is a waste of terminology: super-logarithm grows not faster than the logarithm; the only bigger thing is the rank in the hierarchy, which can be more directly expressed with tetra-.

But we know the drawbacks of "super": it conflicts with our historical use of "super-logarithm" (though I think this was not yet used in published papers) and many dont want to have an arcsuper.

(08/11/2009, 02:14 AM)Tetratophile Wrote: 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?

"tetrational exponential" for a pentational.

And "tetraexponential" or "rank4 exponential" for a tetrational (inside the hyperoperation sequence).

"exponential exponential" or "exp-exponential" for "tetrational" (outside the hyperoperation sequence).

Though one have to adapt to the -power, -exponential, -logarithm terminology, it is quite memorable as one can intuitively give meaning to how to apply the concepts power, exponential and logarithm to the iteration/application of the function to .

They also can be used as shortcut for more classic sounding phrases:

"-power" is short for "functional power of ",

"-logarithm" is short for "functional logarithm of "

etc.

e.g. "tetrational is just another word for functional exponential of the exponential."

Here however we have to be cautious and can not use the term "iterational" instead of "functional" as the phrase "iterative logarithm" is already reserved for the Julia function.

Ya well on the other hand nothing is as succinct as a prefix.