Date: Dec 3, 2012 9:46 AM
Author: Aatu Koskensilta
Subject: Re: Given a set , is there a disjoint set with an arbitrary cardinality?

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, darĂ¼ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus