Definition:Limit Superior of Sequence of Sets/Definition 2

Definition
Let $\set {E_n: n \in \N}$ be a sequence of sets.

Then the limit superior of $\set {E_n: n \in \N}$, denoted $\ds \limsup_{n \mathop \to \infty} \ E_n$, is defined as:
 * $\ds \limsup_{n \mathop \to \infty} \ E_n = \set {x : x \in E_i \text { for infinitely many } i}$

Also see

 * Equivalence of Definitions of Limit Superior of Sequence of Sets