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Cauchy Sequence

  1. Mar 4, 2008 #1
    I'm basically trying to show that if (an) and (bn) are Cauchy sequences, then (cn) = |an - bn| is also a Cauchy sequence.

    I know that the triangle inequality is going to be used at one point or another, but I suppose I'm a little confused because:

    (an) is Cauchy implies |an - am| < e
    (bn) is Cauchy implies |bn - bm| < e

    I think at some point my e's are going to be changed to e/2, which is totally legitimate because e is arbitrary anyway.
  2. jcsd
  3. Mar 4, 2008 #2


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    Science Advisor

    The key to this is to show that ||X|-|Y||<=|X-Y|

    Then ||an-bn|-|am-bm||<=|(an-am)-(bn-bm)|<=|an-am|+|bn-bm|
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