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**seamstress** So basically, I have no idea how to answer this problem. I tried a few different approaches, including trying to show that the complement of A was closed. I am stuck at the very beginning as I do not know where to start with this problem. Could someone please, at the very least, outline what I am supposed to do to prove this? Thank you.

Here's the problem:

Show that $\displaystyle A= \{\frac{1}{n} : n\in N\}$ is not a closed set, but that $\displaystyle A \cup \{0\}$ is a closed set.