Date: Apr 5, 2013 12:04 PM
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.
> > 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.