Definition:Infinite Limit Operator

Definition
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:


 * $\ds \map L {\mathbf x} := \lim_{n \mathop \to \infty} x_n$

Also see

 * Definition:Limit of Sequence