Date: Apr 5, 2013 12:04 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote:
> On Apr 5, 11:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 4 Apr., 23:08, William Hughes <wpihug...@gmail.com> wrote:
>
> > > Nope.  Any single element can be removed.  This does not
> > > mean the collection of all elements can be removed.

>
> > You conceded that any finite set of lines could be removed.  What is
> > the set of lines that contains any finite set? Can it be finite? No.

> correct
> > So the set of lines that can be removed form an infinite set.
>
> More precisely.  There is an infinite set of lines D
> such that any finite subset of D can be removed.


What has to remain?
>
> This does not imply that D can be removed.


> It does however imply that there is no single element
> of D that cannot be removed. That this does not
> imply that D can be removed is a result that
> you do not like, but it is not a contradiction.


It is simple mathological blathering to insist that |N contains only
numbers that can be removed from |N but that not all natural numbers
can be removed from |N.

It is a contradiction with mathematics, namely with the fact that
every non-empty set of natural numbers has a smallest element.

Regards, WM