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Say I have the following

$\bigcap_{n \in \mathbb{N}} \left(-\frac{1}{n}, \frac{1}{n}\right)$

What is the value of this intersection of an infinite amount of open sets?

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    I see you know the answer now. But you might be interested in this: try to find an infinite union of closed sets that is not closed.2013-02-05

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HINT: There is exactly one real number in that intersection: what is it? Once you’ve identified it, you should go on to prove that if $x$ is any other real number, then there is some $n\in\Bbb Z^+$ such that $x\notin\left(-\frac1n,\frac1n\right)$.

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    @dukenukem: Yep, that’s exactly right.2012-10-16