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Sequence convergence

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data
    For any a, b in R, show that ||a|-|b|| <= |a-b|. Then prove that {|s_n|} converges to |L| if {s_n} converges to L.

    2. Relevant equations



    3. The attempt at a solution
    For the first part, ||a|-|b|| = |a-b| by the triangle inequality. For the second part, ||s_n|-0| < epsilon implies that |s_n -0| < epsilon, but I am not sure how to work that around to the L's.
     
  2. jcsd
  3. Sep 29, 2009 #2
    What? For example:
    [itex]\big|\,|2|-|-2|\,\big| = |2-(-2)|[/itex]
    ?????
     
  4. Sep 30, 2009 #3
    Get the [tex]| |a| - |b| | \leq |a - b|[/tex] right first. The second part just follows by the Squeeze Theorem, or more simply, just "shove in the epsilons" if you know what I mean.
     
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