Re: About pii and integers

From: Randy Poe (poespam-trap_at_yahoo.com)
Date: 10/02/04 

Date: 2 Oct 2004 06:21:22 -0700

Keckman <keckman@welho.com> wrote in message news:<opse75q4y03uk9lu@cs81133.pp.htv.fi>...
> On Fri, 01 Oct 2004 13:40:50 -0600, Virgil
> <ITSnetNOTcom#virgil@COMCAST.com> wrote:
>
> > In article <opse61rixm3uk9lu@cs81133.pp.htv.fi>,
> >> Hahaa! So you agree?
> >
> > To what?
> >
>
> "Amount of integers"->oo

The amount of integers is the cardinality of the set N. Whatever
it is, it is fixed. The notation "->" is not meaningful.

> but never ever "amount of integers"=oo

This has two vaguely (in your mind)-defined concepts equated
by an equal sign. We have not agreed what is meant when you
write the thing on the left, nor the thing on the right.

I would say that the set N has a cardinality. I would define
that cardinality to be Aleph-0. I can then explore things about
that cardinality. What I will find is that Aleph-0 > n for
all natural numbers n.

> Because you agree that
>
> none of these wchich are _equal_ does not:
>
> f(n) and n
>
> f(1) = 1
> f(2) = 2
> f(3) = 3
> f(4) = 4
> f(5) = 5
> f(6) = 6
> .
> .
> .
>
> Never n=oo so never f(n)=oo allthough they both ->oo

Yes. n takes on finite values, and so does f(n).

But no value of n is the cardinality of N. So you have not
written anything from which one can conclude things about
the cardinality of N.

           - Randy

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