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Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Posted: Jan 9, 2013 5:11 PM

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

> On 9 Jan., 21:45, Virgil <vir...@ligriv.com> wrote:
>

> > But there are always more subsets of a set than members of that set, so
> > the set of all subsets of a countably infinite set like N will be of
> > greater cardinality than N itself.
> > --

>
> But it does not exist - like the power set of the set of all sets.

The set of all sets is what does not exist, at least not in ZFC and many
other set theories

> Yes, there is an axiom. But it is of same value as the axiom that
> there is a set of all sets

There is no such axiom requiring a set of all sets in many set theories.
Which set theory are you referring to that DOES have such an axiom?

> or the axiom that there is a set of natural
> numbers with cardinality 10 and sum 10.

Those last two axioms may both be required in Wolkenmuekenheim, but they
are not both required anywhere else.

And that last one could only be required in Wolkenmuekenheim.
>
> Regards, WM

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