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Math Help - Sequence of functions

  1. #1
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    Sequence of functions

    Construct a sequence of functions on [0,1] each of which is discontinuous at every point of [0,1] and which converges uniformly to a function that is continuous at every point.

    Can anyone help?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by problem View Post
    Construct a sequence of functions on [0,1] each of which is discontinuous at every point of [0,1] and which converges uniformly to a function that is continuous at every point.

    Can anyone help?
    f_n(x)=\bigg\{\begin{array}{lr}1/n:&x\in\mathbb{Q}\\0:&x\notin\mathbb{Q}\end{array  }
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