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.
So, your use of the term "natural number arithmetic" is meaningless at present.
Let me further applaud you on your adoption of WM's ignorant manner of reply.