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Re: 0^0=1
Posted:
Apr 25, 2012 9:05 AM
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Dan Christensen wrote:
>
> On Apr 24, 4:39 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
> > Dan Christensen wrote:
> >
> > > It isn't included in the usual recursive definition: x^1 = x and x^(n
> > > +1) = x^n * x. And I don't think it can be derived from this
> > > definition. This makes me think it is ad hoc.
> >
> > It's not surprising if a definition of x^n for n = 1, 2, 3, ... cannot
> > reveal what 0^0 is.
> >
>
> Also for n = 0, -1, -2, -3, ...
Ok, I misunderstood your use of the phrase 'recursive definition'.
Let's see how you define x^-3:
x^-3 = x^-4 * x = (x^-5 * x) * x = ...
Compare x^3:
x^3 = x^2 * x = (x^1 * x) * x = (x * x) * x.
The point of recursive definitions, as I understand the phrase, is that
such a sequence comes to an end. In the x^3 case it comes to an end
because the natural numbers are well ordered. In the x^-3 it doesn't
because the integers aren't.
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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