Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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


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

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

Advanced Search
Reply to this Topic Reply to this Topic

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

Posts: 894
Registered: 6/29/05
Re: A size criterion: a question
Posted: Jan 6, 2013 3:07 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jan 6, 1:35 pm, Zuhair <zaljo...@gmail.com> wrote:
> If we characterize cardinality in the following manner, How much that
> would differ from the known cardinality:
>
> |x| < |y| iff there exist an injection from x to y and there do not
> exist a surjection from a subset of x to y.
>
> |x| > |y| iff there exist a surjection from a subset of x to y and
> there do not exist an injection from x to y.
>
> |x| = |y| iff there exist an injection from x to y and there exist a
> surjection from a subset of x to y.

In ZFC there is no difference at all. In ZF there are some striking
differences: under your definition,
(1) |x| > |y| does not imply |y| < |x|;
(2) |x| = |y| does not imply |y| = |x|.

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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.