Partition of an interval
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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{ |xi − xi−1| : i = 1, ..., n }.
As the mesh approaches zero, a Riemann sum based on the partition approaches the Riemann integral.