Let f: [a, b] -> R be function. For r ER, we define following two subsets: U(I) = inf {f(y) | x 0} and An = {r E [a, b] [ U(x) - L(x) > 1}. Show that A = U An. n>1 (d) One can prove that for each n, An is finite (you do not need to show this but this is a good exercise). (e) What do you deduce from (b) (d)