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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 3, 2012 11:54 AM


On 03.12.2012 15:46, Aatu Koskensilta wrote: > jaakov<removeit_jaakov@deleteit_ro.ru> writes: > >> Given a set X and a cardinal k, is there a set Y such that card(Y)=k >> and X is disjoint from Y? > > Yes. > >> Is there a proof of this fact that works without the axiom of >> regularity (= axiom of foundation) and does not assume purity of sets? > > Given a set X pick an object A not in the transitive closure of X and > take Y = { {x,A}  x in X}. >
Y should have cardinality k, not card(X).
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