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  1. The set $S$ of all rational numbers whose denominators are prime.

  2. $S = \{(-1)^{n}+\frac{1}{n}\mid n\in\mathbb{N}\}$

  3. $S = (0,1) $

I have answers for these from the back of a book but I'm not sure about the intuition behind finding the limit points.

Edit: I understand #3 now, all $x\in[0,1]$ are accumulation points since an open ball around any of those points contains infinitely many points of $S$.

Not sure on how to approach #1 though.

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    This community could help you better if you could explain your own thoughts on the problem and where you feel you are stuck.2012-01-24

1 Answers 1