Definition:Norm of Subdivision

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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 $\norm \Delta$.