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How to prove $\limsup(\{A_n \cup B_n\}) = \limsup(\{A_n\}) \cup \limsup(\{B_n\})$? Thanks!

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    Type out the definition of lim sup and the rest is easy.2010-11-07
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    As 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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    @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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    This 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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    I 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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    I started a more general thread about the set-theory tag at http://meta.math.stackexchange.com/questions/1092/appropriate-uses-of-the-set-theory-tag2010-11-08
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    @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

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