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Analysis Proof Help

  1. Oct 8, 2011 #1
    Analysis Proof Help!!

    If anyone could give me a hint on how to start this I would appreciate it! I am struggling with proofs! Thanks!

    Given a sequence (asub(n))
    (i) the sequence is decreasing
    (ii) the limit of the sequence is 0.
    Prove rigorously that an is greater than or equal to 0 for every n contained in the natural numbers
  2. jcsd
  3. Oct 8, 2011 #2
    Re: Analysis Proof Help!!

    [itex]a_n\rightarrow 0[/itex] if [itex]\forall \epsilon >0\exists \bar{n}\backepsilon' \forall n>\bar{n}, |a_n|<\epsilon[/itex].
    Try to prove that, if [itex]a_{\bar{n}}<0[/itex], with a particular choice of epsilon the limit definition is not verified.
    Remember to consider the fact that the sequence is decreasing
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