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