Definition:Limit Superior of Sequence of Sets/Definition 2

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

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

Also see

 * Equivalence of Definitions of Limit Superior of Sequence of Sets