From Wikipedia, the free encyclopedia.
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 the length of the longest of these subintervals; it is max{ xi − xi−1 : i = 1, ..., n }. As the mesh approaches zero, a Riemann sum based on the partition approaches the Riemann integral.
