Question: Suppose that f : [0, 1] R and f(a) = limxa f(x) for all a [0,1]. Prove that f(q) = 0 for all q

Suppose that f : [0, 1] R and f(a) = limx→a f(x) for all a ∊ [0,1]. Prove that f(q) = 0 for all q ∊ Q ∩ [0, 1] if and only if f(x) = 0 for all x ∊ [0, I].

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