Definition:Limit Inferior of Extended Real Sequence

Definition
Let $\sequence {x_n}$ be an extended real sequence.

The limit inferior of $\sequence {x_n}$ is defined as:


 * $\ds \liminf x_n : = \map {\sup_{k \mathop \ge 1} } {\inf_{n \mathop \ge k} x_n}$

Also see

 * Definition:Limit Superior of Extended Real Sequence
 * Existence of Limit Inferior of Extended Real Sequence