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Topic: A size criterion: a question
Replies: 15   Last Post: Jan 9, 2013 1:22 PM

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Posts: 8,833
Registered: 1/6/11
Re: A size criterion: a question
Posted: Jan 7, 2013 4:22 PM
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In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 7 Jan., 19:18, Zuhair <zaljo...@gmail.com> wrote:

> > > In fact, it's consistent with ZF that there are sets x and y such that
> > > both |x| > |y| and |y| = |x|.

> >
> > True, but not in this extension of ZF!
> >

> True, e.g., for indistinguishable reals.
> If you can't distinguish them, you cannot prove that they are more
> than the rationals. |R| = |Q|.
> But if you believe that they exists independently as different numbers
> (although nobody can prove it), then |R| > |Q|.
> Regards, WM

Again, WM is missing the point. Te properties of |x| > |y| and |y| = |x|
depend on the definitions of |x| > |y| and |y| = |x|, and the definition
that Butch and Zuhair re discussing is not the standard one, so that WM
again does not know what he is talking abaout

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