Partition of an interval

This article is about grouping elements of an interval using a sequence. For grouping elements of a set using a set of sets, see Partition of a set.
A partition of an interval being used in a Riemann sum. The partition itself is shown in grey at the bottom, with the norm of the partition indicated in red.

In mathematics, a partition of an interval [a, b] on the real line is a finite sequence x0, x1, x2, …, xn of real numbers such that

a = x0 < x1 < x2 < … < xn = b.

In other terms, a partition of a compact interval I is a strictly increasing sequence of numbers (belonging to the interval I itself) starting from the initial point of I and arriving at the final point of I.

Every interval of the form [xi, xi + 1] is referred to as a subinterval of the partition x.