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Math Help - sequence counterexample

  1. #1
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    sequence counterexample

    Give a counterexample:

    lim sup ( a_n + b_n) = lim sup a_n + lim sup b_n


    Give a proof or counter-example:

    A nested sequence of bounded intervals must have a non-empty intersection.
    Last edited by glasses123; October 23rd 2008 at 04:12 PM.
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  2. #2
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    Quote Originally Posted by glasses123 View Post
    Give a proof or counter-example:
    A nested sequence of bounded intervals must have a non-empty intersection.
    This is a perfect example of where different definitions give different results.
    If we allow that A_n  = \left( {0,\frac{1}{n}} \right) to be a sequence of nested intervals you get one result.
    But many insist that an interval is closed, in that case we get another result.
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