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

Is there a nonempty perfect set in R1 which contains no rational number?

(ex18,chap2,Principles of Mathematics 3rd edition)

2. Relevant equations

3. The attempt at a solution

I tried to prove that there is no such set (because I cannot construct one...) by trying to show that some points in it must be isolated. but a set of \sqrt{2}+1/n (closed but not perfect) prevents me to complete the proof.

Any hint would be appreciated!

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# Homework Help: Problem about perfect set

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