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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 12:34 AM


On Monday, December 3, 2012 6:21:05 AM UTC8, jaakov wrote: > Dear all: > > > > Given a set X and a cardinal k, is there a set Y such that card(Y)=k and > > X is disjoint from Y? > > > > Is there a proof of this fact that works without the axiom of regularity > > (= axiom of foundation) and does not assume purity of sets? > > > > 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?



