\begin{definition}[Definition:Admissible Subdivision for Admissible Curve]
Let $M$ be a smooth manifold.
Let $I := \closedint a b$ be a closed real interval.
Let $\gamma : I \to M$ be an admissible curve. 
Let $\tuple {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ be a finite subdivision of $I$.
Then $\tuple {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ is said to be an '''admissible subdivision''' for $\gamma$.
\end{definition}