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
> 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
all even numbers
Then G has an infinite number of
elements, but you cannot name a single element of G.