Date: Apr 5, 2013 5:50 PM
Author: William Hughes
Subject: Re: Matheology § 224
On Apr 5, 11:03 pm, 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.

>

> Is E restricted to an upper threshold?

> If not, how do you prove its finiteness?

The number of elements in E is a natural number.

No upper limit, but finite.

>

> > Note that whatever

> > subset E is chosen the number of lines

> > in D\E is infinite (but of course we

> > do not know which lines are in D\E).

>

> Can you prove for at least one fixed line that it cannot be removed?

> If not, why do you think that some (even infinitely many) lines must

> remain?

> Don't you feel a bit ridiculous, when you again and again claim

> infinitely many natural numbers none of which you can name?

>

Not at all. Consider a set of natural numbers G.

Let G be

all odd numbers

or

all even numbers

Then G has an infinite number of

elements, but you cannot name a single element of G.