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Topic: Matheology § 293
Replies: 44   Last Post: Jun 27, 2013 2:25 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: WMytheology � 293
Posted: Jun 20, 2013 3:50 PM

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

> On 19 Jun., 23:38, Virgil <vir...@ligriv.com> wrote:
>

> >
> >    The set whose members are {1}, {2}, {3}, ...
> >    clearly has union set |N.

>
> That is just the question.

> >
> > But WM claims
> >    The set whose members are {1}, {1,2}, {1,2,3}, ...
> >    must have a union set strictly less than |N.
> >
> > What sort of set theory says things like that?

>
> Matheology.

No! Only WMytheology.

> The second sequence contains sets such that for every set
> there are aleph_0 numbers missing. The sequence is strictly
> increasing, such that there is never more than one set required to
> have accumulated all numbers of the preceding sets. And every set is a
> union, such that we infinitely many unions. None of which accomplishes
> to yield |N.

The union of all of {1}, {1,2}, {1,2,3}, ...accomplishes
exactly the same as the union of all of {1}, {2}, {3}, ...,
No more and no less, absolutely everywhere except in
WM's wild weird world of WMytheology.
>
> But, abracadabra, if you union the results of infinitely many unions,
> then you get the missing aleph_0 numbers.

If anyone but WM unions all infinitely many sets {1}, {2}, {3}, ...,
they get |N, and since every one of the infinitely many sets,
{1}, {1,2}, {1,2,3}, ... is a proper subset of |N, unioning all of them
cannot give any more than |N.

At least in the correct mathematics outside Wolkenmuekenheim.
>
> That is not correct in mathematics.

It is everywhere outside Wolkenmuekenheim.

Therefore also
>
> {1}, {2}, {3}, ... clearly has not the union set |N - since there is
> no set |N.

There is everywhere outside Wolkenmuekenheim.
>
> Look

We have looked, and find that standard math is justified, but
WMytheology is not.

Note that even Brouwer admits an actual infinity that WM does not.
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