\begin{definition}[Definition:Jordan Arc]
Let $\tuple {x_1, y_1}, \tuple {x_2, y_2} \in \R^2$.
Let $f: \closedint 0 1 \to \R^2$ be a path from $\tuple {x_1, y_1}$ to $\tuple {x_2, y_2}$.
Then $f$ is a '''Jordan arc''' {{iff}} $f$ is an injection, except that we allow the possibility $\tuple {x_1, y_1} = \tuple {x_2, y_2}$.
\end{definition}