Define q(x) = 1 if x ε Q and g(x) = 0 otherwise. Prove that q is not Riemann integrable on {0,1) by showing that for all partitions P
U (q, P) – L(q,P) > 1
I have no idea what I am doing, so any help would be greatly appreciated!
Recall that between any two numbers there is a rational number and an irrational number. Therefore, in any subinterval, P’, of a partition P contains a rational number at which q Is 1 and irrational number at which q is 0. So on P’ the upper sum is 1 and the lower sum is 0.