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Possible Duplicate:
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$

Let $f : [a,b] \to \mathbb Q$ be a continuous function. Prove that $f$ is a constant function.

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    ok thanks @ Asaf Karagila2012-05-13

1 Answers 1

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HINT:

Is $[a,b]$ connected? Is $\mathbb{Q}$?