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Math Help - Riemann integration

  1. #1
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    Question Riemann integration

    Define q(x) = 1 if x ε Q and g(x) = 0 otherwise. Prove that q is not Riemann integrable on {0,1) by showing that for all partitions P
    U (q, P) L(q,P) > 1

    I have no idea what I am doing, so any help would be greatly appreciated!
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  2. #2
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    Recall that between any two numbers there is a rational number and an irrational number. Therefore, in any subinterval, P, of a partition P contains a rational number at which q Is 1 and irrational number at which q is 0. So on P the upper sum is 1 and the lower sum is 0.
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