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
