Dan Christensen wrote: > fom, how about some honest toil to prove 0^0=1? Choose any axioms or definitions you like. Just not 0^0=1 itself or anything like x^0=1 for all x in N. That would be just too easy! ;^)
I think the time has come for you to say what axioms and definition _you_ are using. Let's take first order logic with = for granted, what primitive extra-logical symbols do you have and what extra-logical axioms govern them? If ^ isn't among the primitive extra-logical symbols how is it defined in terms of them?
You have been shown proofs that 0^0 = 1 and you reject them, so what theory (= logical system) of natural numbers do you wish your interlocutors to work in? Spell it out in detail.
That a theory of numbers can be cooked up in which 0^0 = 1 is a wff that can't be proved is clear. But so what?
-- Sorrow in all lands, and grievous omens. Great anger in the dragon of the hills, And silent now the earth's green oracles That will not speak again of innocence. David Sutton -- Geomancies