Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:email@example.com:
> This issue really calls for some > thinking "outside the box."
First, it calls for thinking. You have done none of that yet. If, by some remote miracle, you have a coherent thought someday, then, and only then, we might discuss whether it is in a box or not.
> You yourself have admitted that 0^0 is ambiguous. How do YOU propose > to formalize this ambiguity,
This is, perhaps, the heart of your illogic. "Formalize this ambiguity" is a nonsense phrase. It has no more meaning than "skyblue pink". Second, before one formalizes anything, one ought to have an argument about why it should be formalized at all.
In the context of combinatorics, it's completely logical and completely formal to define 0^0 = 1. And you don't get it.