Definition:Limit Superior/Definition 2

Definition
Let $\sequence {x_n}$ be a bounded sequence in $\R$.

The limit superior of $\sequence {x_n}$ is defined and denoted as:
 * $\ds \map {\limsup_{n \mathop \to \infty} } {x_n} = \inf \set {\sup_{m \mathop \ge n} x_m: n \in \N}$

Also see

 * Equivalence of Definitions of Limit Superior