\begin{definition}[Definition:Limit of Vector-Valued Function/Definition 2]
Let $\mathbf r : \R \to \R^n$ be a vector-valued function.
We say that:
:$\ds \lim_{t \mathop \to c} \map {\mathbf r} t = \mathbf L$
{{iff}}:
:$\forall \epsilon > 0: \exists \delta > 0: 0 < \size {t - c} < \delta \implies \norm {\map {\mathbf r} t - \mathbf L} < \epsilon$
where $\norm {\, \cdot \,}$ denotes the Euclidean norm on $\R^n$.
\end{definition}