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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 3, 2012 9:41 AM
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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?
>
>
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> Thanks in advance
>
>
>
> Jaakov.
>
>
>
> --- news://freenews.netfront.net/ - complaints: news@netfront.net ---

Is this homework?

Consider these two sets: {1,2,3}, {cat, dog, cow}
Then consider the set of even numbers vs the set of odd numbers.
I had to look up "purity of sets". Consider the set of real
numbers in the range [0,1) and the set in the range [1,2).

You might get into a bit of trouble if you tried to find two disjoint
sets with equal cardinality both in the range [0,1]. You'd have
to handle sequenses ending in zeros and those ending in all nines.
Otherwise you could choose a digit and select based upon it being
odd or even.

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

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