Re: About pii and integers

From: Randy Poe (poespam-trap_at_yahoo.com)
Date: 10/01/04 

Date: 30 Sep 2004 17:03:04 -0700

Keckman <keckman@welho.com> wrote in message news:<opse5c3wtg3uk9lu@cs81133.pp.htv.fi>...
> On 30 Sep 2004 08:03:51 -0700, Randy Poe <poespam-trap@yahoo.com> wrote:
>
> Hey come oon boys. The http://www.wordiq.com/definition/Peano_axioms is a
> definition of
> natural numbers. If it does not tell you _nothing_ about natural number
> then what the hell
> you think those natural numbers are?

It tells you a great deal about the natural numbers, which are
the elements of the set N.

You seem unable to distinguish between N and its elements.

You can keep repeating over and over that "every element of N
is finite" means "the set N is finite" but that won't make it
true. Loud rude repetition is not an accepted method of proof.

The Peano axioms tell you about numbers. N is not a number.

>
> How do you define the concept natural numbers if not by Peano's axioms?

That is precisely how we define the natural NUMBERS. Again,
N is not a natural number. It's a set. N is not one of the
objects defined by the Peano axioms. N is the collection
of all the objects which are individually defined by the
Peano axioms.

         - Randy