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jaakov
Posts:
11
Registered:
12/3/12
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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 3, 2012 11:54 AM
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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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