Re: About pii and integers

From: Randy Poe (poespam-trap_at_yahoo.com)
Date: 09/30/04 

Date: 30 Sep 2004 08:03:51 -0700

Keckman <keckman@welho.com> wrote in message news:<opse3sc7g83uk9lu@cs81133.pp.htv.fi>...
> On Tue, 28 Sep 2004 14:58:35 -0500, Daniel W. Johnson
> <panoptes@iquest.net> wrote:
>
> > Induction lets you reach a conclusion about every element of N.
> > It does NOT yield a conclusion about N itself.
>
> Where that's comes from? Is it in the Peano's axioms ?
> (Maybe number 6 has to added to Peanos Axioms)

No, it comes from basic logic. It comes from keeping straight
when you are talking about one object, and when you are
talking about another.

Do you think something that's true about each individual
dog on earth is true of all the dogs on earth?

Keckman logic:

1. Let x be a dog. I can fit x into a cage 2 x 2 x 2 meters.

2. Therefore I can fit all dogs on earth into a cage 2 x 2 x 2 meters.

After reasoning about each individual element of N, you have
learned something about the elements. That does not imply
the set has any particular property. The set is not
the elements. "Any particular dog on earth" is not the
same as "All the dogs on earth".

               - Randy

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