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About the riemann function

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data
    The reimann function (if x is rational then f(x)=1/q, if x is irrational then f(X)=0)is not a step function,then, for any essilope, construct a step function k:[0,1] ~>R s.t. ||f-k||=sup{|f(t)-k(t)|:t is in[0,1]}<essilope,can someone help me to construct such step function


    2. Relevant equations

    suggestion: restrict to q<1/essilope

    3. The attempt at a solution
    my try is f(X)=0 for(0,1) but it seems doesnt work cause when x=1,|f(x)-0|=1>1/2
     
  2. jcsd
  3. Oct 26, 2012 #2
    The given function is not Riemann integrable so it can't be the limit of step functions.
    Maybe you were not accurate in representing the function.what is q?
     
    Last edited: Oct 26, 2012
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