Date: Mar 22, 2013 5:05 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 22 Mrz., 08:30, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 22, 7:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 21 Mrz., 16:41, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 21 Mrz., 14:29, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Mar 21, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > > In fact? That's amazing. So we cannot prove that all lines of the
> > > > > > > > infinite set of lines are unnecessary?

>
> > > > > > > We can prove that something is true for every
> > > > > > > member of an infinite set. We cannot
> > > > > > > prove that something is true for the set
> > > > > > > itself unless the set is finite.

>
> > > > > > But I am not interested in the set itself. Not at all! My claim is
> > > > > > that every member of the set of lines can be removed

>
> > > > > Yes, removed one at a time
>
> > > > > >such that no  member remains
>
> > > > > nope, working one at a time you will not get
> > > > > to the point that no member remains.

>
> > > > Induction does not need time.
> > > > The conclusion from n on n+1, if valid, is valid for every natural at
> > > > one instance.

>
> > > Yes, valid for every natural, but not valid
> > > for the *set* of all naturals.-

>
> > I do not talk about this *set* when removing lines. My proof shows
> > that every line can be removed from the list without removing any
> > natural number from the list.

>
> No your proof shows that *any* *one* line can be removed from the
> list.
> However, you are talking about removing  more
> than one line, i,e. a *set* of lines.


No, I do not speak of a set when I say one, two, or three or
infinitely many lines. Don't confuse the set of all lines with all
lines of the set.

Do you believe that one line can be considered without considering it
as a set, but two or more lines cannot be considered as elements of a
set, but only as the set?
How inconsistent!
And even removing no line cannot be done other than by removing the
empty set?

>  If you want to
> remove all of the lines you have to remove the set of all
> lines that are indexed by a natural number.


But I don't want to remove a set. When has it been prohibited to
handle elements of a set? Where is that laid down in the axioms of
ZFC?

Regards, WM