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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 12:34 AM

On Monday, December 3, 2012 6:21:05 AM UTC-8, jaakov wrote:
> Dear all:
>
>
>
> 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?
2. Are you saying saying k isn't necessarily the cardinality of X?

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?

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