partitionPartition32006-06-09 00:01:412008-02-26 04:17:25Definition% this is the default PlanetMath preamble. as your knowledge
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Let $a,b \in \mathbb{R}$ with $a<b$. A {\sl partition\/} of an interval $[a,b]$ is a set of nonempty subintervals $\{ [a,x_1), [x_1,x_2), \dots , [x_{n-1}, b] \}$ for some positive integer $n$. That is, $a<x_1<x_2<\dots<x_{n-1}<b$. Note that $n$ 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 \PMlinkname{partition}{Partition} of a set since the subintervals are defined so that they are pairwise disjoint.