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

is 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.