Definition:Norm of Subdivision

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Let $\left[{a \,.\,.\, b}\right]$ be a closed interval of the set of real numbers $\R$.

Let $\Delta = \left\{ {x_0, x_1, x_2, \ldots, x_{n-1}, x_n}\right\}$ form a finite subdivision of $\left[{a \,.\,.\, b}\right]$.

Then the norm of $\Delta$ is defined as:

$\max \left\{ {x_1 - x_0, x_2 - x_1, \ldots, x_n - x_{n-1} }\right\}$

and is denoted $\left\Vert{\Delta}\right\Vert$.