\begin{definition}[Definition:Contour/Endpoints/Complex Plane]
Let $C_1, \ldots, C_n$ be directed smooth curves in $\C$.
Let $C_i$ be parameterized by the smooth path $\gamma_i: \left[{a_i \,.\,.\, b_i}\right] \to \C$ for all $i \in \left\{ {1, \ldots, n}\right\}$.
Let $C$ be the contour defined by the finite sequence $C_1, \ldots, C_n$.
The '''start point''' of $C$ is $\gamma_1 \left({a_1}\right)$.
The '''end point''' of $C$ is $\gamma_n \left({b_n}\right)$.
Collectively, $\gamma_1 \left({a_1}\right)$ and $\gamma_n \left({b_n}\right)$ are referred to as the '''endpoints''' of $C$.
\end{definition}