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Thread: Cauchy sequence

  1. December 9th 2012, 10:22 PM #1
    jackie
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    Cauchy sequence

    Would someone help me with this problem?
    Define the sequence \{a_n\} in a metric space (X,d) such that d(a_{n+2},a_{n+1})\leq cd(a_{n+1},a_n) for c\in (0,1). Show that \{a_n\} is Cauchy.
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  2. December 10th 2012, 01:47 AM #2
    emakarov
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    Re: Cauchy sequence

    See the proof of Banach fixed-point theorem.
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