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Topic: 0^0=1
Replies: 15   Last Post: Apr 27, 2012 5:39 AM

 Messages: [ Previous | Next ]
 Frederick Williams Posts: 2,166 Registered: 10/4/10
Re: 0^0=1
Posted: Apr 25, 2012 9:05 AM

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

Date Subject Author
4/25/12 Frederick Williams
4/25/12 Dan Christensen
4/25/12 Frederick Williams
4/25/12 Dan Christensen
4/25/12 Frederick Williams
4/25/12 Dan Christensen
4/27/12 Frederick Williams
4/25/12 Virgil
4/26/12 Jussi Piitulainen
4/25/12 Shmuel (Seymour J.) Metz
4/25/12 Virgil
4/25/12 Frederick Williams