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