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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 21, 2013 3:37 PM

mueckenh@rz.fh-augsburg.de wrote:

> Re: WMytheology § 293
> In article
> WM <muec...@rz.fh-augsburg.de> wrote:
>

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

>
> > The union of all of {1}, {1,2}, {1,2,3}, ...accomplishes
> exactly the same as the union of all of {1}, {2}, {3}, ...,
>
> Yes.
>

> > No more and no less, absolutely everywhere
>
> Yes.
>

> >
> > 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.
>
> Certainly not more, but a lot less.

So, if, according to WM, the union of all FISONs does not include
all of |N, then WM must be claiming that there are natural numbers not
in any FISON.
>
> The sequence of sets is inclusion-monotonic. This means there are never two
> or more sets the union of which surpasses each of the sets.

That only holds for unions of finitely many FISONs, but there are
infinitely many FISONs.
Any and every union of infinitely many FISONs includes all of |N,
at least outside of WM's wild weird world of WMytheology.

>
> The sequence contains only sets each of which lack aleph_0 natural numbers.

The sequence of FISONs contains aleph_0 FISONs, and any and every union
of aleph_0 FISONs contains all of |N.

> Lacking infinitely many natural numbers cannot be compensated by unioning
> infinitely many of such deficient sets.

It can, and does, everywhere outside of WM's wild weird world of
WMytheology.

Consider every FISON reduced to containing only its last and largest
member, then the union of al of them still contains |N.
>
> That's the reason why FredJeffries wished to prohibit sthe union of a sequence
> of sets.
> Unfortunately his desire cannot be granted.

And the union of the sequence of all FISONs still equals |N.
And the union of any infinite sequence of distinct FISONs still equals
|N.

And WM is still totally wrong.
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