On Thursday, September 19, 2013 10:42:09 PM UTC-4, fom wrote: > On 9/19/2013 9:24 PM, Dan Christensen wrote: > > > On Thursday, September 19, 2013 7:36:57 PM UTC-4, fom wrote: > > > > > > Then it should be easy to prove 0^0=1 using only natural number arithmetic. How about it? > > > > > > > One can "prove" nothing to another > > when the latter refuses to provide > > the requested justifications upon > > which the claim of the latter is > > based. > > > > Chicken scratch is not honest toil. > > > > The recursive definition of operations > > follows from Skolem's work. > > > > The class-based definition of 0 > > follows from Frege's work. > > > > You have no definitions. >
Choose any definitions or axioms you like. I'm not fussy. Just don't assume from the start that 0^0=1, e.g that x^0=1 for all natural numbers x.