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Prove a given limit using epsilon-delta

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data

    Suppose that A_n is, for each natural number n, some finite set of numbers in [0,1] and that A_n and A_m have no members in common if m=/n. Define f as follows:

    f(x) = 1/n if x is in A_n
    f(x) = 0 if x is not in A_n for any n

    Prove that the limit of f(x) as x goes to a is zero for all a in [0,1]

    2. Relevant equations
    for every [itex]\epsilon[/itex] there exists a [itex]\delta[/itex] such that
    0<|x-a|<[itex]\delta[/itex] : |f(x)-L|<[itex]\epsilon[/itex]

    3. The attempt at a solution

    Well I'm not even really sure how to start this one so maybe someone could just give me a hint for what to choose as my epsilon and hopefully I can take it from there.
  2. jcsd
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