# 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

R

1

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.

1

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##### Solution Summary

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

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