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Math Help - Sequence Question for Real Analysis

  1. #1
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    Sequence Question for Real Analysis

    Let (x_n) be a sequence of real numbers. Show that either there is some subse-quence (x_nk ) with x_nk --> infinity or with x_nk-->-infinity or there is some subsequence which converges
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    Quote Originally Posted by flaming View Post
    Let (x_n) be a sequence of real numbers. Show that either there is some subse-quence (x_nk ) with x_nk --> infinity or with x_nk-->-infinity or there is some subsequence which converges
    Hint: Every sequence has a monotone subsequence.
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