On Wednesday, October 30, 2013 11:51:13 AM UTC-4, Bart Goddard wrote:
> statements. You're proposing to extend exponentiation from > > N to N_0, but somehow exponentiation isn't extended to 0. >
On the contrary, I have defined exponentiation on all of N_0. 0^0 is assumed to be a natural number. It just hasn't been assigned a value, thus formalizing the longstanding practice of nearly 2 centuries of leaving 0^0 "undefined."
My definition of ^:
1. ^: NxN --> N 2. x^0 = 1 for x=/=0 (note the use of the 0-exponent) 3. x^(y+1) = x^y * x
From this definition, for 0-bases, we can also derive 0^x = 0 for x=/0. So, as usual, your claim is baseless.