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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 5:01 AM
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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?
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