10/13/2008, 07:15 PM

I was just thinking about the following for an arbitrary super exponential :

We surely have for natural numbers m and n that

So why not demand this rule also for the super exponential extended to the reals?

For a super logarithm the rule would be:

Note that this rule is not applicable to the left-bracketed super exponentials.

Because from the rule it follows already that:

which is not valid for left bracketed super exponentials because they grow more slowly.

I didnt verify the rule yet for our known tetration extensions. Do you think it will be valid?

However I dont think that this condition suffice as a uniqueness criterion. But at least it would reduce the set of valid candidates.

We surely have for natural numbers m and n that

So why not demand this rule also for the super exponential extended to the reals?

For a super logarithm the rule would be:

Note that this rule is not applicable to the left-bracketed super exponentials.

Because from the rule it follows already that:

which is not valid for left bracketed super exponentials because they grow more slowly.

I didnt verify the rule yet for our known tetration extensions. Do you think it will be valid?

However I dont think that this condition suffice as a uniqueness criterion. But at least it would reduce the set of valid candidates.