On Thursday, October 17, 2013 4:15:41 PM UTC-4, Bart Goddard wrote: > Dan Christensen <Dan_Christensen@sympatico.ca> wrote in > > news:email@example.com: > > > > >> 3^2 = (0^0)^2 = 0^(2*0) = 0^0 = 3 > > >> > > > > > > Good point! That's why I stipulate that a non-zero base for the Power > > > of a Power Rule (Theorem 5) which you use in your 2nd step. > > > > Which is why you have nothing but contradictions here. You're > > asserting that 0^0 can be defined to be anything, and the > > exponent rules still work.
You can avoid the contradictions by stipulating non-zero bases in each of the Laws of Exponents, as I have done here (see Theorems 4,5 and 7). It's no big deal. While there are still some hold-outs for 0^0=1, mathematicians have been leaving 0^0 undefined in this way for nearly two centuries (starting with Cauchy in the early 19th century).