Let with . A partition of an interval is a set of nonempty subintervals for some positive integer . That is, . Note that is the number of subintervals in the partition.
Subinterval partitions are useful for defining Riemann integrals.
Note that subinterval partition is a specific case of a partition of a set since the subintervals are defined so that they are pairwise disjoint.
![$ [a,b]$](http://images.planetmath.org:8080/cache/objects/7242/l2h/img3.png "$ [a,b]$"){kind=small}
![$ \{ [a,x_1), [x_1,x_2), \dots , [x_{n-1}, b] \}$](http://images.planetmath.org:8080/cache/objects/7242/l2h/img4.png "$ \{ [a,x_1), [x_1,x_2), \dots , [x_{n-1}, b] \}$"){kind=small}
