"Dan Christensen" <Dan_Christensen@sympatico.ca> wrote in message news:firstname.lastname@example.org... > On Saturday, November 16, 2013 12:41:35 PM UTC-5, Bart Goddard wrote: <snip> >> (We'll leave aside the incorrect assumption that leaving >> 0^0 undefined is "common practice.") > > Every high school graduate knows that 0^0 is undefined, but not > necessarily why this is so.
We were simply explained that 0^0 = 0/0, because x^0 = x/x when extending the notion of repeated multiplication to non-positive exponents. Indeed, your rationale for leaving 0^0 undefined isn't different from the one for 0/0, that "every number works": a high school rationale at best.
> Using my approach, it will now be easy to make the case rigorously using > only basic arithmetic. Not everyone will get it (you, for example, Barty), > but I think most will get it right away and wonder what all the fuss was > about.
It is you who keep missing the point: we are not allowed to divide by zero in high school either, yet functions get extended all the time.