# partition

Let $a,b\in\mathbb{R}$ with $a. A 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. 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 Partition1 2013-03-22 15:57:50 2013-03-22 15:57:50 Wkbj79 (1863) Wkbj79 (1863) 8 Wkbj79 (1863) Definition msc 28-00 msc 26A42 subinterval partition Subinterval