Re: infinity
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Thu, 13 Oct 2005 16:52:04 -0600
In article <MPG.1db867f7573cdd9298a48a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> David R Tribble said:
> > Tony Orlow wrote:
> > >> For any finite value you choose, you can find a larger finite
> > >> value, which is still finite, so being larger than any finite
> > >> value you can choose does not make a number infinite.
> > >
> >
> > (I think Tony worded his sentence poorly. His "larger than any
> > finite value you choose" means "larger than any specific finite
> > value you choose", not "larger than all finite values".)
> >
> > That's right; for any finite natural I choose, I can always find
> > another finite natural that is larger than it. And this does not
> > make the larger number infinite. So the set of finite naturals
> > does not contain any infinite values.
> >
> > So how then, Tony, do you get infinite numbers in your set of
> > naturals?
> >
> >
> I can choose a larger value that is infinite, too, so I don't see how
> this has to do with that.
The things that TO does not see encompass almost all of mathematics, and
much of logic as well.
The mechanism for generating the successor of 1 and of any previous
(finite) natural is inherent in Peano, but there is no such
mechanismfor generating any non-finite naturals, and there is a
mechanism for excluding them.
.
- References:
- Re: infinity
- From: Jonathan Hoyle
- Re: infinity
- From: David R Tribble
- Re: infinity
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