# descending order

A sequence or arbitrary ordered set or one-dimensional array of numbers, $a$, is said to be in descending order^{} if each ${a}_{i}\ge {a}_{i+1}$. For example, the aliquot sequence of 259 is in descending order: 45, 33, 15, 9, 4, 3, 1, 0, 0, 0 … The aliquot sequence starting at 60, however, is not in descending order: 108, 172, 136, 134, 70, 74, 40, 50, 43, 1, 0, 0, 0 …

In a trivial sense, the sequence of values of the sign function multiplied by -1 is in descending order: … 1, 1, 1, 0, –1, –1, –1… When each ${a}_{i}>{a}_{i+1}$ in the sequence, set or array, then it can be said to be in strictly descending order.

Title | descending order |
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Canonical name | DescendingOrder |

Date of creation | 2013-03-22 16:06:49 |

Last modified on | 2013-03-22 16:06:49 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 5 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 06A99 |

Related topic | AscendingOrder |

Defines | strictly descending order |