Date: Apr 5, 2013 4:57 PM
Author: Virgil
Subject: Re: Matheology � 224
In article

<560b18fa-164c-4c03-bc3c-2cac32fe9530@j9g2000vbz.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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?

If one has any set, S, which is order isomorphic to the set of naturals

with their natural well-ordering, one can form the family, F, of FISs of

that set (finite initial segments).

Then any infinite subset of F will union to give the original S but no

finite subset of F will union to give back S.

That WM seems incapable of comprehending this simple truth marks his as

mathematically incompetent.

> >

> > 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.

Nonsense, Removing any member of |N from |N leaves a proper subset of |N.

However, removing FISONs from the set of all FISONs of |N may well leave

enough (infinitely many) to have their union equal |N.

Being unable to understand this seems to be WM's personal pons asinorum.

>

> It is a contradiction with mathematics, namely with the fact that

> every non-empty set of natural numbers has a smallest element.

>

Another wild false claim by WM made, as usual, without proof.

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