Partition of an interval

In mathematics, a partition of an interval [a, b] on the real line is a finite sequence of the form a = x₀ < x₁ < x₂ < ... < x_n = b.

Such partitions are used in the theory of the Riemann integral and the Riemann-Stieltjes integral.

The mesh of the partition x₀ < x₁ < x₂ < ... < x_n the length of the longest of these subintervals; it is max{ x_i − x_i−1 : i = 1, ..., n }. As the mesh approaches zero, a Riemann sum based on the partition approaches the Riemann integral.