Partition

Let $I$ be a non-empty, compact interval (closed and bounded). A partition of $I$ is a finite collection $\set{I_1, I_2, \dots, I_n}$ of almost disjoint, non-empty, compact sub-intervals whose union is $I$.

A partition is determined by the endpoints of all sub-intervals: $a=x_0<x_1<\dots<x_n=b$. $$

A partition can be denoted by:

• its intervals - $P=\set{I_1, I_2, \dots, I_n}$
• the endpoints of its intervals - $P=\set{x_0,x_1, \dots, x_n}$