In general, we call
subdivisions of an interval *partitions*. Partitions are usually
specified by giving the set of endpoints of the subintervals, listed in
increasing order, *e.g.* for our example of dividing the interval
[0,4] into 4 equal subintervals we would write .

To describe a general partition of the interval [*a*,*b*], we use
subscript notation, , to denote the *i*-th point in the
partition. That is, a partition with *N* subintervals would be
written , where the points
satisfy

In the case of a uniform partition, there is a simple formula for , which is

For example, there are five points in the uniform partition with four
subintervals of the interval [0,4]. Plugging the values *a*=0,
*b*=4, and *N*=4 into the equation above, we get

Tue Nov 5 14:24:02 EST 1996