Partition of an interval

A finite increasing sequence of points that subdivides a closed interval.

Partition of an interval

A partition of an interval $[a,b]$ is a finite sequence of real numbers

P=\{x_0,x_1,\dots,x_n\}\quad\text{with}\quad a=x_0<x_1<\cdots<x_n=b.

The associated subintervals are $[x_{i-1},x_i]$ for $i=1,\dots,n$ .

Partitions of the interval $[a,b]$ are used to build Riemann sums and the upper /lower sums that define the Riemann integral .

Examples:

The uniform partition of $[0,1]$ into $n$ pieces is $P=\{0,\tfrac1n,\tfrac2n,\dots,1\}$ .
A non-uniform partition of $[0,3]$ is $P=\{0,\tfrac12,1,3\}$ .