\begin{definition}[Definition:Limit Inferior of Sequence of Sets/Definition 2]
Let $\sequence {E_n : n \in \N}$ be a sequence of sets.
Then the '''limit inferior''' of $\sequence {E_n : n \in \N}$, denoted $\ds \liminf_{n \mathop \to \infty} E_n$, is defined as:
:$\ds \liminf_{n \mathop \to \infty} E_n := \set {x: x \in E_i \text { for all but finitely many } i}$
\end{definition}