Is $\{12,18\} \cup ([-6,6] \setminus(-2,2))$ a compact set? Is the following set of real numbers compact?
$$\{12,18\} \cup ([-6,6] \setminus(-2,2))$$ 
It is obviously bounded (upper bound is $18$, lower bound is $-6$) but is it closed? I am not so familiar with topologic terms so please apologize if this question may seem a little dumb.

Yes, it's closed. Your set can be written as $\{12,18\} \cup [-6,-2]\cup [2,6]$ and thus it is closed as finite union of closed sets.
