\begin{definition}[Definition:Continuous Mapping (Metric Space)/Point/Definition 2]
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.
Let $f: A_1 \to A_2$ be a mapping from $A_1$ to $A_2$.
Let $a \in A_1$ be a point in $A_1$.
$f$ is '''continuous at (the point) $a$ (with respect to the metrics $d_1$ and $d_2$)''' {{iff}}:
:$(1): \quad$ The limit of $\map f x$ as $x \to a$ exists
:$(2): \quad \ds \lim_{x \mathop \to a} \map f x = \map f a$.
\end{definition}