The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 18,076
Registered: 1/29/05
Re: A size criterion: a question
Posted: Jan 7, 2013 1:23 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 7 Jan., 19:18, Zuhair <> 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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.