On Friday, November 1, 2013 4:14:52 PM UTC-4, Bart Goddard wrote:
> Your version of "thinking" results in > > contradictions.
No contradictions here.
> > >> 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. > > >> > > > > > > That's absurd! > > > > Not hardly. You seem to think that we've been plodding > > along all these centuries without a formal notion of > > something. (Assuming this were true, (it's certainly not)) > > why bother formalizing it now? >
To understand exactly why 0^0 should be left undefined and how to work with this notion in practice.
> >> In the context of combinatorics, it's completely logical > >> and completely formal to define 0^0 = 1. And you don't > >> get it. > > > First of all, you don't need combinatorics (or cardinality) to > > > construct an exponent-like function ^ on N such that 0^0=1. > > At no point did I suggest using combinatorics to construct > > anything.
Apparently you don't understand how functions are formally constructed. See, for example, the construction on the 'pow' function in my Theorem 1. You could probably use some recursion theorem to shorten it considerably, but it works as is.