Science Fair Project Encyclopedia
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{ |xi − xi−1| : i = 1, ..., n }.
As the mesh approaches zero, a Riemann sum based on the partition approaches the Riemann integral.
Last updated: 08-22-2005 18:39:36
11-30-2008 18:11:33
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details