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


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?



