partition

Let $a,b\in ℝ$ with . A partition of an interval $[a,b]$ is a set of nonempty subintervals $\{[a,x_1),[x_1,x_2),\mathrm{\dots },[x_{n-1},b]\}$ for some positive integer $n$. That is, . 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