> [!NOTE] Definition (Partition) > A *[[Finite Set|finite]] [[Partition of a Set|partition]]* of a *[[Real intervals|bounded interval]]* $I$ is a finite set $P$ of bounded intervals contained in $I,$ such that every $x \in I$ lies in exactly one of the bounded intervals $J\in P.$ > **Notation**: we may denote a partition $P$ of $[a,b]$ by its set of endpoints $P=\{ x_{0},x_{1},x_{2},\dots,x_{n-1},x_{n} \}$ where $a=x_{0}<x_{1}<x_{2}<\dots<x_{n-1}<x_{n}=b.$