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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 3, 2012 9:41 AM
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On Monday, December 3, 2012 6:21:05 AM UTC-8, jaakov wrote:
> Dear all:
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> Given a set X and a cardinal k, is there a set Y such that card(Y)=k and
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> X is disjoint from Y?
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> Is there a proof of this fact that works without the axiom of regularity
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> (= axiom of foundation) and does not assume purity of sets?
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> Thanks in advance
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> Jaakov.
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> --- news://freenews.netfront.net/ - complaints: news@netfront.net ---
Is this homework?
Consider these two sets: {1,2,3}, {cat, dog, cow}
Then consider the set of even numbers vs the set of odd numbers.
I had to look up "purity of sets". Consider the set of real
numbers in the range [0,1) and the set in the range [1,2).
You might get into a bit of trouble if you tried to find two disjoint
sets with equal cardinality both in the range [0,1]. You'd have
to handle sequenses ending in zeros and those ending in all nines.
Otherwise you could choose a digit and select based upon it being
odd or even.
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