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    Real Analysis: Riemann Integrability

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    Let E = { 1/n : n 2 N } . Prove that the function
    f(x) =
    1 x 2 E
    0 otherwise
    is integrable on [0,1]. What is the value of
    0 f(x)dx?
    Since this problem is an analysis problem, please be sure to be rigorous.
    It falls under the chapter on Integrability on R , where they define partition,
    refinement of a partition, upper and lower Riemann sums, (Riemann)
    integrability, and upper and lower integrals in terms of the infimum and
    supremum of the respective sums.

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    Solution Summary

    A function is proven to be Riemann integrable. The solution is detailed and well presented.