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Limits of sequences of subsets

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm just trying to find liminf and limsup for:

    2. Relevant equations

    [tex]E_n = (n, n+2)[/tex]

    3. The attempt at a solution

    Since every subset occurs a finite number of times, would I say that limsup is the empty set? Is being bounded by nothing the same thing as being bounded by infinity?

    For liminf:

    [tex]((1,3)\cap(2,4)\cap...)\cup((2,4)\cap(3,5)\cap...)\cup...[/tex]

    I ended up with [tex][2,∞)[/tex]
     
  2. jcsd
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