Re: Proposed definition for comparing the sizes of two sets

From: Dan Christensen (dchris_at_netcom.ca)
Date: 11/30/04 

Date: 30 Nov 2004 12:25:11 -0800

"Shmuel (Seymour J.) Metz" <spamtrap@library.lspace.org.invalid> wrote in message news:<41ab8d88$5$fuzhry+tra$mr2ice@news.patriot.net>...
> In <4b0c747b.0411282057.3a22c922@posting.google.com>, on 11/28/2004
> at 08:57 PM, dchris@netcom.ca (Dan Christensen) said:
>
> >Proposed Definition: A set Y is said to be larger than a set X iff
> >there exists no function mapping X onto all of Y. (i.e. there is no
> >surjection from X to Y)
>
> >Is this a workable definition that covers all cases? If so, is it
> >widely used?
>
> Are you assuming the Axiom of Choice, or some equivalent? If not, you
> have to deal with incomparable pairs of sets.

I don't currently have AC built into my program, but you can introduce
it as a premise at the beginning of any proof. I am planning to make
it a true axiom, as well as building in some defintions for cardinal
numbers in a future release. Some details need to be worked out.

Dan
Download DC Proof 1.0 at http://www.dcproof.com