$\mathbb{N}$ is a Compact Space with the Co-finite Topology?

Question

Let $X$ be the topological space on the set $\mathbb{N}$ with the cofinite topology.

I am having a hard time seeing why this is compact in the topological sense. If each open $n$-hood on $X$ contains all but finitely many elements of $\mathbb{N}$ Then how can a finite subcover exist? I can see how the complement of each of my neighbourhoods could be compact, is that somehow the same thing?

Answer 1

HINT: For every open set there are only finite number of $n$'s not covered by it.