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I cant see the logic of thes definitions

  1. Mar 16, 2009 #1
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 16, 2009 #2

    matt grime

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    It isn't the supremum of the limits.

    Lim sup means the limit of the supremums. I.e. the reverse of what you were thinking.

    You .gif is too small to be read, at least by me.
     
  4. Mar 16, 2009 #3
    Last edited by a moderator: May 4, 2017
  5. Mar 16, 2009 #4

    matt grime

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    Last edited by a moderator: May 4, 2017
  6. Mar 16, 2009 #5
    her is the definition that i got
    http://img23.imageshack.us/img23/6383/18151267.gif [Broken]
     
    Last edited by a moderator: May 4, 2017
  7. Mar 16, 2009 #6
    He is using an example, this is not a definition. limsup is the limit supremum, that is the limit of the supremums (supremums are a decreasing function on n). In that case the sequence oscillates, so the supremum is 1 and infemum is -1, hence limsup=1 and liminf=-1.

    The wiki article is correct. I think the picture is more helpful to remember these.
     
    Last edited by a moderator: May 4, 2017
  8. Mar 16, 2009 #7

    matt grime

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    It doesn't even make sense to take the supremum of limits. Why?

    If x_n converges to x, then so does every subsequence, so sups of any sequence of limits can only be x. Conversely, if x_n does not converge, then you don't have limits of which you can take the sups....
     
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