# monotonically nondecreasing

A sequence $({s}_{n})$ (with real elements) is called *monotonically nondecreasing* if

$${s}_{m}\ge {s}_{n}\forall m>n$$ |

Similarly, a real function $f(x)$ is called monotonically nondecreasing if

$$f(x)\ge f(y)\forall x>y$$ |

Compare this to monotonically increasing.

Conflict note. In other contexts, such as [1], this is called *monotonically increasing* (despite the fact that the sequence could be “flat.” In such a context, our definition of “monotonically increasing” is called *strictly increasing*.

## References

- 1 “http://www.nist.gov/dads/HTML/monotoncincr.htmlmonotonically increasing,” from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.

Title | monotonically nondecreasing |
---|---|

Canonical name | MonotonicallyNondecreasing |

Date of creation | 2013-03-22 12:22:38 |

Last modified on | 2013-03-22 12:22:38 |

Owner | akrowne (2) |

Last modified by | akrowne (2) |

Numerical id | 8 |

Author | akrowne (2) |

Entry type | Definition |

Classification | msc 40-00 |

Synonym | monotone nondecreasing |

Related topic | MonotonicallyNonincreasing |