Date: Mar 23, 2013 5:21 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<3929c991-8368-4c1d-a111-9c187a37aa0f@l9g2000yqp.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.



Yes it is, since it always requires that one start with all infinitely
many lines and remove only finitely many of them.


> 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.


Maybe WM thinks he can prove that, but he cannot do so anywhere outside
of his wild weird world of Wolkenmuekenheim, because when one starts
outside his wild weird world of Wolkenmuekenheim with an infinitely sets
each of evens and odds, removing only finitely many from either, or
both, leaves the two sets equally large, still countably infinite.
>
> > 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.


Then why have you claimed otherwise?




>
> I have shown that, given actual infinity, we can delete all *finite*
> lines without changing the union of all lines of the list.


WM has shown no such thing. Every line/FISON is finite even when there
are infinitely many of them.

WM is actually claiming to be able to remove every member of an
non-empty set and still have the emptied set non-empty.

What at most is true is that one can delete any set of ALL BUT
infinitely many lines/FISONs, and still have all naturals left.

This is because EVERY infinite set of lines/FISONs collectively contains
all naturals but NO finite set of lines/FISONs collectively contains all
naturals
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