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Topic: Matheology � 258
Replies: 53   Last Post: May 11, 2013 10:07 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 258
Posted: May 7, 2013 3:47 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 7 Mai, 10:09, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 7 Mai, 00:14, Dan <dan.ms.ch...@gmail.com> wrote:
> >
> > > > 0.11111......
> > > > should also be a valid real number .
> > > > Infinite digits ,corresponding to an infinite row, are as valid as
> > > > infinite digits of the columns .

> >
> > > 0.11111...... it is not in the list
> >
> > > 0.1
> > > 0.11
> > > 0.111
> > > ...

> >
> > But, just like |N is the limit of the sequence of FISONs,
> > it is the limit of your sequence.
> >

> The union of lines
> cannot contain more elements than one line contains.

Why not?

Unless there is some line that contains all other lines as subsets,
it is inevitable that the union contain more than any one line.

Note that, at least outside of Wolkenmuekenheim, in any union of any
family of sets, unless one of those sets already contains all the others
as subsets, the union must always contain more than any single one of
the sets being unioned. But according to WM that does not happen in
Wolkenmuekenheim.

Thus the WM's religion, WMytheology, cannot apply anywhere outside of
Wolkenmuekenheim.

On the other
> hand, according to set theory, the union of all lines contains more
> indices, namely |N, than than all lines. Contradiction.

Only more than in any line, which is quite different.

At least outside of WMytheology.

Theorem true everywhere except in Wolkenmuekenheim:
Given a family of sets in which each set of the family is
a proper subset of some other set of the family,
then every set in the family is a proper subset of the
union of that family.
--