\begin{definition}[Definition:Infinite Limit Operator]
Let $c$ be the space of convergent sequences.
Let $\mathbf x := \sequence {x_n}_{n \mathop \in \N} \in c$.
Let $\R$ be the set of real numbers.
The '''infinite limit operator''', denoted by $L$, is the mapping $L : c \to \R$ such that:
:$\ds \map L {\mathbf x} := \lim_{n \mathop \to \infty} x_n$
\end{definition}