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What is the difference in of the two questions:

Q1: If the function $f: [a;b]\to \mathbb{R}$ is continuous that takes only rational values. Show that $is$ is constant.

Q2. If $f:[a,b]\to\mathbb{R}$ is a continuous function and $f(x)\in\mathbb{Q}$ for all $x\in[a,b]$. Then show that $f$ is a constant function.

Are the both problem same? What is the meaning of takes only rational values. Q2. is solved in Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?.

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rama_ran
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    Yes they're both the same. Takes only rational values means that $f(x)$ is rational for every $x$ in $[a,b]$. You can prove it with the intermediate value theorem. – Ethan Alwaise Apr 09 '17 at 17:23

1 Answers1

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Yes they are the same. It is just some wording difference. A function taking only on rational values means its functional values are and only are rational numbers.

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