(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose f:[a,b]->R is continuous and that f([a,b]) is a subset of Q (rational numbers). Prove that f is constant on [a,b]

2. Relevant equations

N/A

3. The attempt at a solution

The solution states that:

f([a,b]) must contain only one point, because if it has more than that, then it would have to be an irrational point. Which is a contradiction.

My questions are, why does f([a,b]) contain only one rational point? Why can't it be a collection of rational points?

Thank you for your help.

M

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# Homework Help: Analysis Question -

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