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