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Math Help - Bounded Sequence

  1. #1
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    Bounded Sequence

    Give an example of bounded sequence that does not converge.
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    The most straightforward one :

    (-1)^n
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  3. #3
    Super Member redsoxfan325's Avatar
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    Non-convergent Cauchy sequences will be bounded as well.
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    Quote Originally Posted by redsoxfan325 View Post
    Non-convergent Cauchy sequences will be bounded as well.
    For this to work you must be working in a non-complete metric space. So this isn't going to happen in \mathbb{R}^n
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  5. #5
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by putnam120 View Post
    For this to work you must be working in a non-complete metric space. So this isn't going to happen in \mathbb{R}^n
    We aren't in \mathbb{R}^n.
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