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

Iff: ℝ → ℝ is a continuous function with the property that its range is contained in the set of integers, prove thatfmust be a constant function.

2. Relevant equations

3. The attempt at a solution

I know why this is true, I just don't know how to begin an actual proof. So far I've thought of proving by contradiction, with letting f be discontinuous and usef(x) = [x], whose range set is contained in Z.

I seem to have trouble with the format of a formal proof.

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# Prove that f must be a constant function

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