\begin{definition}[Definition:Limit of Mapping between Metric Spaces]
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.
Let $c$ be a limit point of $M_1$.
Let $f: A_1 \to A_2$ be a mapping from $A_1$ to $A_2$ defined everywhere on $A_1$ ''except possibly'' at $c$.
Let $L \in M_2$.
$\map f x$ is said to '''tend to the limit $L$ as $x$ tends to $c$''' and is written:
:$\map f x \to L$ as $x \to c$
or:
:$\ds \lim_{x \mathop \to c} \map f x = L$
{{iff}} the following equivalent conditions hold:
\end{definition}