# partition

Let $a,b\in \mathbb{R}$ with $$. A partition^{} of an interval $[a,b]$ is a set of nonempty subintervals $\{[a,{x}_{1}),[{x}_{1},{x}_{2}),\mathrm{\dots},[{x}_{n-1},b]\}$ for some positive integer $n$. That is, $$. 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 partition (http://planetmath.org/Partition) of a set since the subintervals are defined so that they are pairwise disjoint.

Title | partition |
---|---|

Canonical name | Partition1 |

Date of creation | 2013-03-22 15:57:50 |

Last modified on | 2013-03-22 15:57:50 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 8 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 28-00 |

Classification | msc 26A42 |

Synonym | subinterval partition |

Related topic | Subinterval |