Question: 6. (10 points) Define f : R - R by f(x) = 1 if x is irrational, f(x) = 0 if x is rational. Prove

6. (10 points) Define f : R - R by f(x)

6. (10 points) Define f : R - R by f(x) = 1 if x is irrational, f(x) = 0 if x is rational. Prove that there exists a sequence {In } converging to a real number ro such that In * To for all n E R and such that the sequence f(In) - f(To) is unbounded

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