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Thread: Subsquence

  1. #1
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    Talking Subsquence

    Prove: If F is a complete Archimedan field, then every bounded sequnce in F has a subsequence that converges in F.
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  2. #2
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    Quote Originally Posted by tigergirl View Post
    Prove: If F is a complete Archimedan field, then every bounded sequnce in F has a subsequence that converges in F.
    I am assuming that the field is real numbers.
    The key to showing this is to first prove this lemma: Every sequence contain a monotonic subsequence.
    Then you should proved that every bounded monotonic sequence converges.
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