\begin{definition}[Definition:Limit of Function (Normed Vector Space)]
Let $M_1 = \struct {X_1, \norm {\,\cdot\,}_{X_1}}$ and $M_2 = \struct {X_2, \norm {\,\cdot\,}_{X_2}}$ be normed vector spaces.
Let $c$ be a limit point of $M_1$.
Let $f: X_1 \to X_2$ be a mapping from $X_1$ to $X_2$ defined everywhere on $X_1$ ''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}