08/29/2007, 06:14 PM

I have to admit I never considered the case , but I recently discussed it with Gianfranco.

We know that is no more injective if we allow this range.

If we consider one rank below the ordinary exponentiation, we have a similar case there, that is no more defined for , because is not injective for so . This gives also trouble as then .

On the other hand for tetration is *not* the inversion of . So the rules may be a bit different here.

So what do you think how tetration looks for ? And what role plays the range ?

We know that is no more injective if we allow this range.

If we consider one rank below the ordinary exponentiation, we have a similar case there, that is no more defined for , because is not injective for so . This gives also trouble as then .

On the other hand for tetration is *not* the inversion of . So the rules may be a bit different here.

So what do you think how tetration looks for ? And what role plays the range ?