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 $\displaystyle \liminf_{n \to \infty} \ E_n$, is defined as:


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

Also see

 * Equivalence of Definitions of Limit Inferior of Sequence of Sets