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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 6:09 AM

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. 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.

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

That is not correct in mathematics. Therefore also

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

Look, if after the end of all times God will check what natural
numbers have been used by his creatures, then the set will be finite.
That means, at least in mathematics, there has no actually infinite
set |N been applied over the aeons. Mathematicians could have chosen
every natural they wish. Nevertheless, all belong to a set that has
aleph_0 elements less than what you define as |N.

Regards, WM

Regards, WM