Date: Jun 11, 2013 6:06 PM
Subject: Re: Matheology ? 285
In article <firstname.lastname@example.org>, Sam Sung <email@example.com>
> Virgil schrieb:
> > In article <firstname.lastname@example.org>,
> > email@example.com 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.
> > 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.