\begin{definition}[Definition:Limit Inferior/Definition 2]
Let $\sequence {x_n}$ be a bounded sequence in $\R$.
The '''limit inferior of $\sequence {x_n}$''' is defined and denoted as:
:$\ds \map {\liminf_{n \mathop \to \infty} } {x_n} = \sup \set {\inf_{m \mathop \ge n} x_m: n \in \N}$
\end{definition}