partition

Let $a,b\in\mathbb{R}$ with $a<b$ . A partition of an interval $[a,b]$ is a set of nonempty subintervals $\{[a,x_{1}),[x_{1},x_{2}),\dots,[x_{n-1},b]\}$ for some positive integer $n$ . That is, $a<x_{1}<x_{2}<\dots<x_{n-1}<b$ . Note that $n$ is the number of subintervals in the partition.

Subinterval partitions are useful for defining Riemann integrals.

Note that subinterval partition is a specific case of a partition (http://planetmath.org/Partition) of a set since the subintervals are defined so that they are pairwise disjoint.

Title	partition
Canonical name	Partition1
Date of creation	2013-03-22 15:57:50
Last modified on	2013-03-22 15:57:50
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	8
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 28-00
Classification	msc 26A42
Synonym	subinterval partition
Related topic	Subinterval