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.

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