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I cant understand this liminf/sup definition

  1. Jan 8, 2009 #1
    i got this new definition

    http://img515.imageshack.us/img515/5666/47016823jz1.gif

    what is the meaning of n>=0 under a sup.
    sup is not a limit
    its only a number
    we cant put index under it
    what is the meaning of this indexes?
     
    Last edited: Jan 8, 2009
  2. jcsd
  3. Jan 8, 2009 #2

    tiny-tim

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    Hi transgalactic! :smile:

    Under the sup is n ≥ 0, not n -> 0.

    anything with a -> (such as n -> 0) would be a limit, as you know …

    anything without a -> (such as n ≥ 0) means that that is the range over which the sup is taken …

    in other words, if you rewrite it inside {}, then it finishes with : n ≥ 0} :wink:
     
  4. Jan 8, 2009 #3
    i cant imagine what you are saying

    can you rewrite the definition
     
  5. Jan 8, 2009 #4

    HallsofIvy

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    "sup" is a property of a set. [itex]sup_{n\ge m} {a_n}[/itex] is the supremum of the set {a_m, a_{m+1}, a_{m+2}, ...}.
     
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