Date: Mar 23, 2013 5:56 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 23 Mrz., 21:54, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 23, 4:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 23 Mrz., 15:01, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 23, 2:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 23 Mrz., 10:31, William Hughes <wpihug...@gmail.com> wrote:
> > > > > 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.
>
> > > WH: this does not mean that one can do something
> > > WH: that does not leave any of the lines of K
> > > WH: and does not change the union of all lines.

>
> > > WM: That is clear
>
> > Please complete this sentence: "That is clear because my proof rests
> > upon the premise that actual infinity is a meaningful notion."

>
> > If actual infinity was existing as a meaningful notion, then we could
> > remove all finite lines without changin the union in any way.

>
> nope
> actual infinity existing as a meaningful notion, does not mean
> we could remove all finite lines without changing the union
> in any way.


Do you think it is not a contradiction, to have the statements:
1) 0.111... has more 1's than any finite sequence of 1's.
2) But if we remove all finite sequences of 1's, then nothing remains.
>
> You have agreed that, "under the assumption that actual
> infinity is a meaningful notion"
> you have not shown that we could remove all finite lines
> without changing the union in any way.


You reverse the facts. Under this assumption I have shown precisely
that.
And you have acknowledged my proof:

WH: Yes, given any set of lines K, every element of K has the property
that it can be removed without changing the union of all lines. Yes,
the set of lines that has this property is the complete set K.

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

This is a clear contradiction (garnished with the false quote of mine
on top of this page).
Of course in set theory we can construct the set of all finite lines
which are subject to my proof. Of course we can subtract ithis set
from the list that contains all natural numbers. Of course that does
what my proof shows, namely no change in the numbers of the list.
Otherwise my proof would be wrong and not acceptable by you.

Do you wish to withdraw your approval?

Regards, WM