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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: WMytheology § 293
Posted: Jun 20, 2013 12:40 PM

On 20 Jun., 17:10, FredJeffries <fredjeffr...@gmail.com> wrote:
> On Jun 20, 3:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>

> > But, abracadabra, if you union the results of infinitely many unions,
> > then you get the missing aleph_0 numbers.

>
> No. You do not do infinitely many unions. That is nonsense.
>
> You do ONE union.

You seem to have not yet understood. But I enjoy to explain it again,
and again, and again, ... because the story is incredible.

Every set of the sequence

1,
1, 2
1, 2, 3
...

is the union of all its predecessors and its last {n}.

There are infinitely many sets, so there are infinitely many unions.

None of these infinitely many unions yields |N, although every union

After you pause, exhausted, since you failed to get |N but got only
sets which a lacking aleph_0 natural numbers, you pray and do a last
union. This last union cannot supply anything new, because the union
of a set with its subsets cannot yield a larger set. (And we know,
none of the sets is |N. All sets are subsets of one set. Each of the
sets is infinitely far away from being |N.) But your prayer has been
accepted. The last union, you would not believe it, yields |N.

I love this story!

Regards, WM