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