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Math Forum » Discussions » sci.math.* » sci.math.independent

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

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mueckenh@rz.fh-augsburg.de

Posts: 12,658
Registered: 1/29/05
Re: A size criterion: a question
Posted: Jan 7, 2013 1:23 PM
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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

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