# 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 < ... < xn = 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 < ... < xn

is the length of the longest of these subintervals; it is

max{ |xixi−1| : i = 1, ..., n }.

As the mesh approaches zero, a Riemann sum based on the partition approaches the Riemann integral.

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