This is review from class the other day that I managed to miss because of illness and I was wondering if someone could explain how to go about solving these problems:(adsbygoogle = window.adsbygoogle || []).push({});

#1

Let

[tex]B = \left\{ \frac{(-1)^nn}{n+1}:n = 1,2,3,...\right\}[/tex]

Find the limit points of B

Is B a closed set?

Is B an open set?

Does B contain any isolated points?

Find [tex]\overline{B}[/tex].

#2

Let [tex]a \in A[/tex]. Prove thatais an isolated point of A if and only if there exists an [tex]\epsilon[/tex] neighborhood [tex]V_\epsilon(a)[/tex] such that [tex]V_\epsilon(a) \bigcap A = \left\{a\right\}[/tex].

#3 - This is a proof the class worked on:

A set [tex]F \subseteq \texttt{R}[/tex] is closed if and only if every Cauchy sequence contained in F has a limit that is also an element of F.

This is all that was talked about according to the professor, and there were some other examples shown of the first problem. I suppose that since I wasn't there in class, I have less of an edge than those who were, so I'd love to see how and more precisely why things work the way they do. Help would be greatly appreciated!

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# Limit Points

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