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