Let f, g be continous from R to R and suppose f(r)=g(r) for all rational numbers r. Is it true that f(x) = g(x) for all x in R. R - real numbers I need a proof of why this is true or if false a counterexample with proof.
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Originally Posted by hayter221 Let f, g be continous from R to R and suppose f(r)=g(r) for all rational numbers r. Is it true that f(x) = g(x) for all x in R. R - real numbers I need a proof of why this is true or if false a counterexample with proof. If then there is a sequence with such that . Then by continuity and . But . Thus, .
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