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Pointwise convergence

  1. Jan 6, 2010 #1
    This has stuck with me for a long time, i just cant do it.

    If the sequence of functions, fn(x): R+ --> R

    where fn(x) is defined as

    fn(x) = x/n if 0 is greater than and equal to x, x is less than and equal to n

    fn(x) = 1 if x is strickly greater than n


    I need to show that the fn(x) is pointwise convergence so the zero function. f(x) =0
     
  2. jcsd
  3. Jan 6, 2010 #2

    Dick

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    Pick any x0>0 and epsilon>0. Find an N such that for all n>N, f_n(x0)<epsilon. Surely you can at least TRY and start.
     
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