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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 12:34 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
Based upon some of your replies I have a question.
Given your statment: "Given a set X and a cardinal k"
1. Are you referring to any set X or specifically a set of real numbers?
2. Are you saying saying k isn't necessarily the cardinality of X?
Given your question "> Is there a proof of this fact that works without
the axiom of regularity (= axiom of foundation) and does not assume
purity of sets?
1. Are you referring to any set or specifical sets of real numbers?
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