Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    mathman

    User Avatar
    Science Advisor
    Gold Member

    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|
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Cauchy Sequence
  1. Cauchy sequence (Replies: 2)

  2. Cauchy sequence (Replies: 10)

  3. Cauchy Sequences (Replies: 4)

  4. Cauchy sequence (Replies: 6)

  5. Cauchy Sequences (Replies: 4)

Loading...