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