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Topic:
Given a set , is there a disjoint set with an arbitrary cardinality?
Replies:
28
Last Post:
Dec 4, 2012 5:50 PM



jaakov
Posts:
11
Registered:
12/3/12


Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 6:38 AM


>> Let A be an infinite set with max{ X, k }< A. >> Since k< A = A\X, take Y to be any subset of >> A\X with Y = k. >> > This is all very true intuitively. I'd like to be sure that the claims > > X<A => A = A\X > > k<B => exists Y subset B such that Y=k > > are valid without the regularity and purity axioms. I am not asking you > to provide the corresponding proofs, I am just wondering whether you > know that. > > In any case, we already have several ways of proving the original claim. > I think that these claims to not depend on regularity or purity.
Jaakov.



