Show $\{-n + 1/n \ : n \in \mathbb{N}\}$ is a closed set I have the set 
$$A = \{-n + 1/n \ : n \in \mathbb{N}\}$$ 
My attempt
I tried to find some limit point in A, but
$$
\lim_n (-n + 1/n) = -\infty
$$
Is there anyone to help?

The complement of $A$ is $\bigcup_{n\in\mathbb N}(-n-1+\frac1{n+1},-n+\frac1n)\bigcup(0,+\infty)$, which is a union of open intervals, thus open. Therefore $A$, as the complement of an open subset, is closed.

Hope this helps.
