Date: Mar 23, 2013 9:43 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 23 Mrz., 10:31, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 23, 9:26 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 22 Mrz., 23:33, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 22, 11:10 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 22 Mrz., 22:50, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Mar 22, 10:42 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > On 22 Mrz., 22:31, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > On Mar 22, 10:14 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 22 Mrz., 21:33, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > <snip>
>
> > > > > > > > > this does not mean that one can do something
> > > > > > > > > that does not leave any of the lines of K
> > > > > > > > > and does not change the union of all lines.

>
> > > > > > > > That is clear
>
> > > > > > > So stop claiming your proof
> > > > > > > means you can do something
> > > > > > > that does not leave any of the lines
> > > > > > > of K and does not change the union
> > > > > > > of all the lines.

>
> > > > > > My proof is this: IF there is an actually infinite list of FISONs as I
> > > > > > devised it, THEN all lines can be removed without changing the union
> > > > > > of the lines.

>
> > > > > You have shown that any FISON and all preceding
> > > > > FISONs can be removed

>
> > > > given the premise that set |N, the union of all FISONs, is "more" than
> > > > every FISON.

>
> > > > > You have agreed that you have not shown you can do
> > > > > something  that does not leave a FISON
> > > > > and does not change the union of all the lines

>
> > > > Yes. And you have approved my proof. But we know both that the result
> > > > is wrong

>
> > > No, we both agree that the result is correct
> > > And we both agree that the result does not
> > > lead to a contradiction.-

>
> > So you believe that we can remove all lines without changing the
> > union?

>
> Nope.
>
> We both agree that you have shown we can remove
> any line without changing the union.


And this proof is not restricted to the case that always a line
remains.
If it was restricted, as you seem to believe without eveidence, then
also the following case would be true:

We prove that every odd number has an even number as follower, but
nevertheless there are less (or more, as you like) even than odd
numbers.

> We both agree that you have not shown that we can
> do something which leaves no lines and does not
> change the union.


No, of course we do not. If you believe so, it is up to you. But if
you want to make a *mathematical* claim of this kind, then you have to
show which lines have to remain or, if you cannot, you have to show at
least why any finite line has to remain. If the only reason is to keep
set theory free of contradictions, then your argument may hold in
matheology but not in mathematics.

I have shown that, given actual infinity, we can delete all *finite*
lines without changing the union of all lines of the list. This is as
clear as we can be sure that every natural number is finite.

Regards, WM