Date: Mar 22, 2013 2:24 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 22 Mrz., 16:24, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 22, 10:01 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 22 Mrz., 08:19, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 22, 7:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 21 Mrz., 16:46, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Mar 21, 2:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > > But you think that after all finite and unnecessary lines another one
> > > > > > > > is lurking like a dragon?

>
> > > > > > > Now I think that after any finite set of unnecessary lines has
> > > > > > > been removed, there still remains an unnecessary line.-

>
> > > > > > 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.

>
> > > > > Nope.  I only talk about removing finite sets of ordinary
> > > > > elements.  I do not talk about removing all ordinary elements.

>
> > > > 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.-

>
> > And what is in your opinion beyond any finite set of lines?
>
> There is no such thing
> as "beyond every finite set of lines".


Therefore your objection is wrong.

> Infinite sets are different from finite sets
> but they do not contain anything
> "beyond any finite set".


Of course. But if they don't, then we have only all finite paths in
the Binary Tree, to name only one problem. This shows that ll paths
are countable.

> Some infinite sets of lines can be removed without changing
> the contents, some cannot.


Yes, actual infinity requires doing mathematics "nach Gutsherrenart".
But not many mathematicians will agree to work without general rules..

Regards, WM