Prove that there does not exist a continuous function f:R-->R satisfying f(Q)$\displaystyle \subset$ R\Q and f(R\Q)$\displaystyle \subset$Q.

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- Nov 18th 2011, 02:38 PMwopashuiprove there is no such continuous function
Prove that there does not exist a continuous function f:R-->R satisfying f(Q)$\displaystyle \subset$ R\Q and f(R\Q)$\displaystyle \subset$Q.

- Nov 18th 2011, 02:43 PMTheChazRe: prove there is no such continuous function
I have proven it. What is your next command?