Need help analysing a particular set

[man0005]

Homework Statement

For the set S = (-1)^n * (3 + 5/n)
I have determined that the maximum is 3 + 5/2 and the minimum is -8. However I am not sure if it is closed; given that it has a maximum and minimum, does this mean by definition that the set will be closed?

Homework Equations

The Attempt at a Solution

 

[hilbert2]

The number 3 is a limit point of the set, which means that for any $\epsilon>0$ we have a value $x\in S$ such that $|x-3|<\epsilon$. However, 3 itself is not contained by the set $S$. Search with google for "closed set limit points" and you will find the answer to your question.