Date: Jun 11, 2013 6:06 PM
Author: Virgil
Subject: Re: Matheology ? 285

In article <kp8645$g5h$1@speranza.aioe.org>, Sam Sung <no@mail.invalid> 
wrote:

> Virgil schrieb:
>

> > In article <c5bb02d5-fd32-4b10-a052-e61af7d4d02e@googlegroups.com>,
> > mueckenh@rz.fh-augsburg.de wrote:
> >

> >> On Tuesday, 11 June 2013 19:18:34 UTC+2, Julio Di Egidio wrote:
> >>

> >>> > Therefore it is not possible to enumerate all rational numbers >
> >>> > (always
> >>> > infinitely many remain) by all natural numbers (always > infinitely
> >>> > many
> >>> > remain) or to traverse the lines of a Cantor list (always > infinitely
> >>> > many remain).

> >>
> >>> It is not possible to do so effectively... Julio
> >>
> >> It is only possible by applying the axiom of infinity.

> >
> > Surjecting the naturals onto the rationals is usually done by formula,
> > of which formulae many are already known.

>
> Right - even little things and concepts as are continuous functions
> require the existence of "actual" infinity.
>
> http://de.wikipedia.org/wiki/Stetigkeit_(Topologie)
>

> > The existence of such surjections can also be proved by injecting the
> > rationals into the naturals, which is even easier.

>
> nbl You really write very considerable posts - easy learning,
> simply great, thx


I keep trying to write things so simply and straightforawardly that even
WM will be unable to garble them, but with WM I fail.
--