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.

You can express it as a finite union of closed sets. Notice
$$[-6,6] \setminus (-2,2) = [-6,-2] \cup [2,6]$$
so
$$\{12,18\} \cup ([-6,6] \setminus (-2,2)) = \{ 12 \} \cup \{ 18 \} \cup [-6,-2] \cup [2,6]$$
A finite union of closed sets is closed, so your set is closed.
It's clearly bounded since it's contained in the set $[-6,18]$.
