Definition 14.5.1 (Limit of Sets). Let $X$ be a set and $\seq{E_n}\subset 2^{X}$, then the limit superior of $\seq{E_n}$ is
\[\limsup_{n \to \infty}E_{n} = \bigcap_{n \in \natp}\bigcup_{k \ge n}E_{k}\]
and the limit inferior of $\seq{E_n}$ is \[\liminf_{n \to \infty}E_{n} = \bigcup_{n \in \natp}\bigcap_{k \ge n}E_{k}\]