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    Ruler function proof

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    Define Ruler Function g:(0,1)-> R (it is the usual ruler function available online)

    as g(x) = { 1/q if x = p/q, p and q are relatively prime
    { 0 if x is irrational.

    Show (without using Riemann-Lebesgue Theorem) that g is Riemann integrable.

    The hint says that since L (lower sum) is zero, it remains to show that U (Upper sum) is less than epsilon for some partition p. I'm trying to do that, but to me the answer is elusive.

    © BrainMass Inc. brainmass.com October 9, 2019, 10:16 pm ad1c9bdddf
    https://brainmass.com/math/computing-values-of-functions/ruler-function-proof-214560

    Solution Preview

    Hello

    Please find the solution in the attached files.

    Proving Ruler Function is Riemann Integrable without using Riemann-Lebesgue Theorem
    Define Ruler Function g:(0,1)-> R (it is the usual ruler function available online)

    as g(x) = { 1/q if x = p/q, p and q are relatively ...

    Solution Summary

    This provides an example of proving the Ruler Function is Riemann Integrable without using Riemann-Lebesgue Theorem.

    $2.19