Constructing a Step Function for the Riemann Function with Restrictions on q

[cummings12332]

Homework Statement

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

Homework Equations

suggestion: restrict to q<1/essilope

The Attempt at a Solution

my try is f(X)=0 for(0,1) but it seems doesn't work cause when x=1,|f(x)-0|=1>1/2

 

[hedipaldi]

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?