Asked by Jacob
Prove that the function defined by:
f(x)={1 if x is rational, 0 if x is irrational
is not integrable on [0,1]. Show that no matter how small the norm of the partition, ||P||, the Riemann sum can be made to have value either 0 or 1.
f(x)={1 if x is rational, 0 if x is irrational
is not integrable on [0,1]. Show that no matter how small the norm of the partition, ||P||, the Riemann sum can be made to have value either 0 or 1.
Answers
Answered by
Steve
a simple google on the question turns up many discussions of the problem and its proof.
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