In article <email@example.com>, Peter Percival <firstname.lastname@example.org> wrote:
> Dan Christensen wrote: > > > > > I have shown that we need only explicitly define ^ in N for exponents > > of 2 or more. > > Actually you haven't, you have shown that in that case 0^0 might be > either of 0 and 1.
However limited it may be, it is still a definition, just a limited one.
> So your "definition" leaves x^y undefined at one > point; therefore it is no definition. The purpose of a definition is to > give the thing defined a precise meaning, you haven't given 0^0 a > precise meaning. > > > Apart from the base of 0, > > Why apart from? Why are you leaving it out? What is even odder, having > left it out you seem to think that 0^0 being undefined is a good thing. > No it isn't, it's a job half done.
So is leaving out a definition of division by zero also a job half done? > > > we can derive values for > > exponents 0 and 1. In that sense, the usual definition has redundant > > elements. > > >> > > > > Many standard textbooks leave 0^0 undefined. This is not the realm of > > cranks or radicals. On the contrary, it is the most conservative > > option. > > Are they talking about x^y on the reals? --