Re: About pii and integers

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

Date: 30 Sep 2004 17:07:11 -0700

Keckman <keckman@welho.com> wrote in message news:<opse5d51ri3uk9lu@cs81133.pp.htv.fi>...
> On Wed, 29 Sep 2004 16:57:21 -0600, Virgil
> <ITSnetNOTcom#virgil@COMCAST.com> wrote:
>
> > In article <opse3ralsc3uk9lu@cs81133.pp.htv.fi>,
> > There is no contradiction in having an infinite set whose elements are
> > all finite.
>
> Not. Really there have not been.
>
> But it is too simpple. Don't just read this fast bye.
>
> Take a look at this f(n)=n. Where f(n) is a amounts n's precessor.
> What happenens to the f(n) when n->oo ?

More than likely you misunderstand what the notation "n->oo"
means. It does not mean n is ever infinite. It means that
n is allowed to take on any finite value, no matter how
large.

What happens to f(n) as n takes ever larger FINITE values is
that f(n) also takes ever larger FINITE values. And never is
it infinite.

>
> Can n->oo ?

Yes, since that notation means "n increases without bound". It
doesn't mean "n gets to infinity".

> Allmost that is used everywhere in math. n->oo

Yes, it is used many places in math. It tells you about
behavior at large finite values.

Here is a more technical description of "n->oo". Let M
be any finite value. Then eventually n will exceed M.

Note that the word "infinite" or "infinity" does not
appear there.

>
> If you claim that f(n)=oo

I certainly would never claim that.

> then you claim too that there is n=oo.

Nor would I claim that.

       - Randy

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