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Let f, g : R → R be continuous functions. (a) Prove that if f(r) = 0 for all r ∈ Q, then f(x) = 0 for all x ∈ R. (b) Prove that if f(r) = g(r) for all r ∈ Q, then f(x) = g(x) for all x ∈ R.
How should I go about this problem using sequences? For example, can I form a sequence r-sub-n —-> x and somehow use that show f(x) = 0?