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Math Help - are there two continuous functions in [0,1] satisfies these conditions

  1. #1
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    are there two continuous functions in [0,1] satisfies these conditions

     \int_{0}^{1}{|f-g|}=0
    but
     \sup_{x\in[0,1]}{|f-g|}>0

    f,g are two continuous functions on [0,1]
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  2. #2
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    You know that if f\;\&\;g are continuous functions then \left| {f - g} \right| is also a continuous function.
    If a continuous function is positive at any point in [0,1] then the function is positive throughout some subinterval.
    What does that say about the integral?
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