Let f ( x ) = {0, if x = 1/n for some natural number n(adsbygoogle = window.adsbygoogle || []).push({});

or 1, otherwise

Note: Natural number would refer to the set of positive integers Z+ that is 1,2,3,...

Prove that this function is integrable on [0,1] and it's integral is 1

Certainly there are an infinite number of dicontinuities and nearly all of the function lies in the domain of [0,1]. But is the set of Inverse Naturals (1/n) (postive integers) bigger than the set of irrationals?

Someone recommended using the Robustness of the Reimann Integral

Let g and f be two functions defined on [a,b], and suppose

that the set of numbers in [a,b] at which the functions do not

take the same value (at which they "differ") is finite.

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# Could someone give me an idea for a proof of this

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