> > There is nothing weird about my number system. Again, the notion that > 0^0 is undefined is not some new, radical idea. It has been around > for centuries and is really quite mainstream. (See that Wiki article > I cite above.)
Your reading comprehension is poor. 0^0 on the reals is a different kettle of fish from 0^0 on the natural numbers. Are you still talking about the latter? Your subject header suggests so.
> If you polled all the world's math instructors, I am > sure that the vast majority would agree that 0^0 should be left > undefined.
I am not, so proof by being sure isn't a very good kind of proof.
-- Sorrow in all lands, and grievous omens. Great anger in the dragon of the hills, And silent now the earth's green oracles That will not speak again of innocence. David Sutton -- Geomancies