suppose that $f$ is continuous on [a,b], and the range of $f$ consists of the whole Rational numbers,
prove that $f$ is a constant function
Help, Please?
2026-04-02 20:05:50.1775160350
Mean Value theorem, continuity...
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Hint If $f$ takes two different rational values $a$ and $b$, by the Intermediate Value Theorem it takes all values in between.
Hint 2 There exists irrational numbers between $a$ and $b$. For example $a+\frac{1}{\sqrt{2}}(b-a)$.