Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:email@example.com:
> If, for some reason, you don't want to call it a definition, call it a > theorem.
No. It is neither. It's a bit of empty stupidity. You're claiming to extend exponentiation to N_0, but all of your rules say "nonzero base." It's a monument of idiocy, the likes of which mankind has never before seen. If you keep saying "nonzero base", then you haven't done anything about 0, so there is no extention.
>In practice, it makes no difference.
Of course it makes a difference. If you extend exponentiation to N_0, then 0^0 has to mean something, if you make it mean anything but 0 or 1, then you get contradiction. Of 0^0 doesn't mean anything, then you haven't done any extending.