This is the definition of accumulation point that my book gives:(adsbygoogle = window.adsbygoogle || []).push({});

A is an accumulation point of [tex]S \subset \mathbb{R}, \forall \epsilon > 0, S \bigcap B(A;\epsilon)[/tex] is infinite.

The book I have gives horrible examples on what accumulation points actually are (contradicting itself two out of the three times), but never actually gives instructions on how to find the points.

This is the question I have to solve:

Find the accumulation points of

[tex]S = \left\{\frac{2}{n} + (1 - \frac{1}{n})cos(\frac{n\pi}{2}) : n \in\mathbb{N}\right\} [/tex]

Can anyone help to actually explain to me, in english, what an accumulation point is? I tried Wikipedia but it's more of this meaningless jargon.

Hopefully, understanding what it is I'm looking for will show me how to answer this question. If not, I could use help there too.

I'd post some relevant work I've done on this problem, but I really have no idea where to start! Why can't analysis books ever actually explain things as if I might actually not understand their initial rambling?

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# Accumulation points and finding them

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