How to prove $\limsup(\{A_n \cup B_n\}) = \limsup(\{A_n\}) \cup \limsup(\{B_n\})$? Thanks!
Proof: Limit superior intersection
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elementary-set-theory
limits
limsup-and-liminf
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1Type out the definition of lim sup and the rest is easy. – 2010-11-07
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1As pointed out in an answer, the "lim sup" operation requires some sort of limit - a sequence, for example, What do you mean by the lim sup of a set? – 2010-11-07
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0@Carl Mummert: It doesn't really make sense as a real-analysis problem with unions; it makes more sense as a problem of sequences of sets. So I would not exchange the set-theory tag for the real-analysis tag. – 2010-11-07
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0This question has absolutely *nothing* to do with set theory. People tend to misuse the set-theory tag for any question that involves sets, but that is just as silly as adding "abstract algebra" to any question that involves addition. – 2010-11-08
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0I have no idea whether the "sequences-and-series" tag would apply. @gaer: could you please clarify what the question is about? – 2010-11-08
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0I started a more general thread about the set-theory tag at http://meta.math.stackexchange.com/questions/1092/appropriate-uses-of-the-set-theory-tag – 2010-11-08
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0@gaer: The union of families *also* does not make sense. Presumably, you meant the family of unions, and I've edited as such. – 2010-11-08