On Wednesday, September 11, 2013 5:09:52 PM UTC-4, Peter Percival wrote: > Dan Christensen wrote: > > > > > > > > Show me a contradiction that arises from 0^0 = 0. > > > > The product of the empty set is 1, hence 0^0 = 1. That contradicts 0^0 > > = 0. Therefore 0^0 doesn't = 0. >
You are talking about some other set-theoretic notion of exponentiation, not the usual arithmetic operator that we are discussing here.
More convincing would be obtaining a contradiction by assuming only 0^0=0 along with the usual rules of natural-number arithmetic, including the usual Laws of Exponents.