Date: Apr 6, 2013 6:30 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 6 Apr., 00:12, Virgil <vir...@ligriv.com> wrote:
> In article
> <f5967d16-5eda-4a94-8b9f-0a0f57aeb...@r7g2000vbw.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 5 Apr., 21:03, William Hughes <wpihug...@gmail.com> wrote:
> > > On Apr 5, 6:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote:
>
> > > <snip>
>
> > > > > There is an infinite set of lines D
> > > > > such that any finite subset of D can be removed.

>
> > > > What has to remain?
>
> > > This depends on the finite subset removed.
> > > If the finite set removed is E then
> > > D\E has to remain.  Note that whatever
> > > subset E is chosen the number of lines
> > > in D\E is infinite

>
> > How do you call a set E the number of elements exceeds any given
> > natural number?

>
> Infinite!
>
>
>

> > >  (but of course we
> > > do not know which lines are in D\E).

>
> > How do we call a set when we cannot biject it with a FIS on |N?
>
> Infinite!


So the set E of all lines that can be removed is infinite, like every
inductive set, by the way, and like the set that contains {a} if it
contains a.

But according to WH these sets are finite. It is only a small problem,
that we do not know and cannot determine the finite number of their
elements and the last element.

Regards, WM