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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 4, 2012 6:38 AM
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>> 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.
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