On Wednesday, October 30, 2013 5:15:24 PM UTC-4, Bart Goddard wrote: > Dan Christensen <Dan_Christensen@sympatico.ca> wrote in > > news:email@example.com: > > > > > > >> You're claiming to extend exponentiation to N_0, but > > >> > > >> all of your rules say "nonzero base." > > > > > > [snip] > > > > > > Nothing wrong with that. > > > > In mathematics, contradiction is the ONLY sort of wrong > > there is. And you're definitely contradicting yourself. > > You're extending without extending. >
Call it what you will, but I have put on a rigorous mathematical basis the longstanding practice (nearly two centuries) of leaving 0^0 undefined. And we still have x^0 = 1 and 0^x = 0 for all natural numbers x=/=0.
If you find this "inconvenient," that really is too bad. Learn to deal with it, Barty.