1. Let ƒ be a continuous function on R such that f(q) = 0 for all rational numbers q E Q. Prove that f(x) = 0 for all r € R. Hint: Let r be an arbitrary irrational number. Recall Q is dense in R. This means there is a sequence of rational number q„ such that qn → r. Now use sequential continuity to show f(r) = 0.

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Q: #1. ii. Thanks

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