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