Infinite subset of R contains a non-empty open interval I'm preparing for the exam, trying to solve this. Every infinite subset of R contains a non-empty open interval. Every infinite subset of R contains a non-empty closed interval. Every infinite subset of R has a non-empty closed subset. Which one of these are true? If false can you give counterexamples?

Hints:

* For the first two, consider the set of integers.$\\\\[4pt]$
* For the third one, note that a singleton set is closed.