\begin{definition}[Definition:Norm of Subdivision]
Let $\closedint a b$ be a closed interval of the set of real numbers $\R$.
Let $\Delta = \set {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ form a finite subdivision of $\closedint a b$.
Then the '''norm''' of $\Delta$ is defined as:
:$\max \set {x_1 - x_0, x_2 - x_1, \ldots, x_n - x_{n - 1} }$
and is denoted $\norm \Delta$.
\end{definition}