Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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: Given a set , is there a disjoint set with an arbitrary cardinality?
Replies: 28   Last Post: Dec 4, 2012 5:50 PM

Advanced Search

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

Posts: 1,243
Registered: 1/8/12
Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted: Dec 4, 2012 1:29 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 3 Dec 2012, forbisgaryg@gmail.com wrote:
> On Monday, December 3, 2012 6:21:05 AM UTC-8, jaakov wrote:

> > Given a set X and a cardinal k, is there a set Y such that card(Y)=k and
> >
> > X is disjoint from Y?
> >
> > Is there a proof of this fact that works without the axiom of regularity
> >
> > (= axiom of foundation) and does not assume purity of sets?

>
> Based upon some of your replies I have a question.
>
> Given your statment: "Given a set X and a cardinal k"
>
> 1. Are you referring to any set X or specifically a set of real numbers?


Any set or course.

> 2. Are you saying saying k isn't necessarily the cardinality of X?

That's right.
All that was said about the given cardinal k was card Y = k.

> Given your question "> Is there a proof of this fact that works without
> the axiom of regularity (= axiom of foundation) and does not assume
> purity of sets?
>
> 1. Are you referring to any set or specifical sets of real numbers?


Any set of course. No where was it stated or even suggested
that X or Y, is a subset of the reals. Where do you get this
notion that the discussion is about set of real numbers?



Date Subject Author
12/3/12
Read Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
forbisgaryg@gmail.com
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Aatu Koskensilta
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Carsten Schultz
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Aatu Koskensilta
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Aatu Koskensilta
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Carsten Schultz
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Aatu Koskensilta
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Butch Malahide
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/3/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Butch Malahide
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
forbisgaryg@gmail.com
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
William Elliot
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
forbisgaryg@gmail.com
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
William Elliot
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
William Elliot
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
William Elliot
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Shmuel (Seymour J.) Metz
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Spammer
12/4/12
Read Re: Given a set , is there a disjoint set with an arbitrary cardinality?
jaakov

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.