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jaakov
Posts:
11
Registered:
12/3/12
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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 5:22 AM
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On 04.12.2012 11:01, William Elliot wrote:
> On Mon, 3 Dec 2012, 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?
>
>
> Case |X|< k. Let Y be a set with |Y| = k.
> |Y\X| = k; Y\X and X are disjoint.
> Case |X|<= k. Let A be a set with k< |A|. k< |A| = |A\X|.
> Take Y as any subset of A\X with |Y| = k.
>
>> Is there a proof of this fact that works without the axiom of regularity (=
>> axiom of foundation) and does not assume purity of sets?
Thank you!
Jaakov.
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