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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 3, 2012 9:46 AM
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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}.
--
Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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