Definition:Norm of Subdivision

Definition

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 $\norm \Delta$.

Sources

• 2011: Robert G. Bartle and Donald R. Sherbert: Introduction to Real Analysis (4th ed.): $\S 7.1$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): partition (of an interval)