Definition:Limit Superior of Extended Real Sequence

Definition
Let $\left \langle {x_n} \right \rangle$ be an extended real sequence.

The limit superior of $\left \langle {x_n} \right \rangle$ is defined as:


 * $\displaystyle \limsup x_n : = \inf_{k \mathop \ge 1} \left({\sup_{n \mathop \ge k} x_n}\right)$

Also see

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