Date: Mar 22, 2013 3:19 AM
Author: William Hughes
Subject: Re: Matheology § 224
On Mar 22, 7:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 21 Mrz., 16:46, William Hughes <wpihug...@gmail.com> wrote:

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> > On Mar 21, 2:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

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> > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:

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> > > > > But you think that after all finite and unnecessary lines another one

> > > > > is lurking like a dragon?

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> > > > Now I think that after any finite set of unnecessary lines has

> > > > been removed, there still remains an unnecessary line.-

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> > > I know. That's what I wished to prove. In order to believe in the

> > > existence of actually infinite sets, it is necessary to have another

> > > element after all ordinary elements have been removed.

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> > Nope. I only talk about removing finite sets of ordinary

> > elements. I do not talk about removing all ordinary elements.

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> Do you know that set theory is timeless? Induction holds for all

> natural numbers (not for the set though - but that is out of

> interest). This proves that we can remove all finite lines from the

> list without changing the contents of the remaining list.

No, it only proves that you can remove any finite

set of lines.