partition of an interval

In mathematics, a partition of an interval \[\left[ a,b \right]\] on the real line is a finite sequence \[x_{0},x_{1},x_{2},\dots,x_{n}\] of real numbers such that \[a=x_{0}<x_{1}<x_{2}<\dots<x_{n}=b\]. In other words, a partition of a compact interval \[I\] is a strictly increasing sequence of numbers starting form the initial point of \[I\] and arriving at the final point of \[I\].

Every interval of the form \[\left[ x_{i},x_{i+1} \right]\] is referred to as a sub-interval of the partition \[x\].