\begin{definition}[Definition:Limit Superior of Extended Real Sequence]
Let $\sequence {x_n}$ be an extended real sequence.
The '''limit superior''' of $\sequence {x_n}$ is defined as:
:$\ds \limsup x_n : = \map {\inf_{k \mathop \ge 1} } {\sup_{n \mathop \ge k} x_n}$
\end{definition}