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Math Help - bounded sequences

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    bounded sequences

    Show that a bounded sequence in R that does not converge has more than one subsequential limit. That is, show that a nonconvergent bounded sequence has two subsequences each with a different limit.
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    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by Jdg6057 View Post
    Show that a bounded sequence in R that does not converge has more than one subsequential limit. That is, show that a nonconvergent bounded sequence has two subsequences each with a different limit.
    I'd try by absurd : Suppose that every subsequences of the bounded sequence converge to the same limit. If you can show that the sequence converges then you're done.
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