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Real analysis proof with sequences

  1. Dec 5, 2009 #1
    1. The problem statement, all variables and given/known data
    Let Sn be a sequence in R

    Prove lim Sn= = 0 if and only if lim abs(Sn) = 0

    2. Relevant equations

    none

    3. The attempt at a solution

    I think this is someone ciruclar logic and that is why I am stuck

    Assume lim Sn = 0, thus for n > N implies |Sn| < epsilon or -epsilon < Sn < epsilon. Since Sn and -Sn are less than epsilon |Sn| < Epsilon for sufficently large n.
    Now assume lim |Sn|= 0 so ||Sn||< epsilon and using a similar arguement show Sn < Epsilon and complete the proof. IS that the way to go?
     
  2. jcsd
  3. Dec 5, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    It's not circular, it's just that proving Sn->0 and |Sn|->0 are pretty much the same thing. Yes, that's the way to go.
     
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