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

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 forbisgaryg@gmail.com Posts: 43 Registered: 11/26/12
Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted: Dec 4, 2012 3:20 AM

On Monday, December 3, 2012 10:29:36 PM UTC-8, William Elliot wrote:
> 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?
>
> > >
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> > > Is there a proof of this fact that works without the axiom of regularity
>
> > >
>
> > > (= axiom of foundation) and does not assume purity of sets?
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> >
>
> > Based upon some of your replies I have a question.
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> >
>
> > Given your statment: "Given a set X and a cardinal k"
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> >
>
> > 1. Are you referring to any set X or specifically a set of real numbers?
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>
>
> 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?

So, what is the cardinality of the universal set?

As was noted no set can be a member of itself.

(Ex ~xeU) <=> ~(Ax xeU)

Can a subset of the universal set have the same
cardinality as the universal set? Since neither
X nor Y are identified, suppose X is the universal set.
Can there be a disjoint set Y let alone one with cardinality
k?

Maybe I saw the asnwer in other replies but didn't notice it.
The syntax being used is a bit strange but seems to be often
used by many.

Date Subject Author
12/3/12 jaakov
12/3/12 forbisgaryg@gmail.com
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Carsten Schultz
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Carsten Schultz
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 Butch Malahide
12/3/12 jaakov
12/3/12 Butch Malahide
12/4/12 jaakov
12/4/12 forbisgaryg@gmail.com
12/4/12 William Elliot
12/4/12 forbisgaryg@gmail.com
12/4/12 William Elliot
12/4/12 William Elliot
12/4/12 jaakov
12/4/12 William Elliot
12/4/12 jaakov
12/4/12 Shmuel (Seymour J.) Metz
12/4/12 Spammer
12/4/12 jaakov