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Math Help - Prove every unbounded seq. contains a monotone subseq. that diverges to infinity

  1. #1
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    Prove every unbounded seq. contains a monotone subseq. that diverges to infinity

    Could anyone explain to me how I would go about proving such a statement? Thank you and good day.
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  2. #2
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    Quote Originally Posted by binkypoo View Post
    Could anyone explain to me how I would go about proving such a statement? Thank you and good day.

    Hint: let {x_n} be the unbounded seq. Choose x_n(1) to be s.t. x_n(1) > 1; now choose x_n(2) so that x_n(2) > max{ x_n(1), 2},....etc.
    Can you see WHY can we always choose as above and how this solves the problem?

    Tonio
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