
Re: The ambiguity of 0^0 on N
Posted:
Sep 19, 2013 5:04 PM


Dan Christensen wrote: > On Thursday, September 19, 2013 4:20:17 PM UTC4, Peter Percival wrote: >> Dan Christensen wrote: >> >>> On Thursday, September 19, 2013 11:41:47 AM UTC4, Helmut Richter wrote: >> >>>> On Thu, 19 Sep 2013, Dan Christensen wrote: >> >>>> >> >>>> >> >>>> >> >>>>> Again, the notion of 0^0 being undefined is not some radical notion. >> >>>> >> >>>>> Many standard textbooks make this assumption. It is probably more >> >>>> >> >>>>> mainstream than assuming 0^0=1. I'm sure that a poll of all math >> >>>> >> >>>>> instructors would confirm this. >> >>>> >> >>>> >> >>>> >> >>>> At least it makes the definition of power series easier. Would you like to >> >>>> >> >>>> see >> >>>> >> >>>> >> >>>> >> >>>> e^x = Sum(i=0,...) x^i/i! for x!= 0 >> >>>> >> >>>> = 1 for x = 0 >> >>>> >> >>>> >> >>> >> >>> Yeah, it could get ugly, but until we can actually prove that 0^0=1 from first principles, this would be the prudent thing to do. >> >> >> >> The first principle is the definition of x^y, but when I prove 0^0 = 1 >> >> from the definition in two lines you object. What you seem to object to >> >> is that it is just two lines. >> > > So, why don't we just include Goldbach's Conjecture in the axioms of number theory and move on?
Because we don't yet know that Goldbach's conjecture is true. But a more significant point so far as the discussion of 0^0 is concerned is this: Goldbach's conjectute isn't a definition.
 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

