Definition:Limit Inferior of Sequence of Sets/Definition 2

Definition
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:


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

Also see

 * Equivalence of Definitions of Limit Inferior of Sequence of Sets