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jaakov
Posts:
11
Registered:
12/3/12


Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 5:22 AM


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.



