Definition:Limit Inferior of Sequence of Sets/Definition 2

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

Then the limit inferior of the sequence, denoted $\displaystyle \liminf_{n \mathop \to \infty} \ E_n$, is defined as:


 * $\displaystyle \liminf_{n \mathop \to \infty} \ E_n := \set {x: x \in E_i \text{ for all but finitely many } i}$

Also see

 * Equivalence of Definitions of Limit Inferior of Sequence of Sets