# monotonically increasing

A sequence $({s}_{n})$, ${s}_{n}\in \mathbb{R}$ is called *monotonically increasing* if

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

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

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

Compare this to monotonically nondecreasing.

Conflict note. This condition is also sometimes called *strictly increasing* [1]. In such a context, “monotonically increasing” has the same meaning as monotonically nondecreasing.

## References

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

Title | monotonically increasing |
---|---|

Canonical name | MonotonicallyIncreasing |

Date of creation | 2013-03-22 12:22:35 |

Last modified on | 2013-03-22 12:22:35 |

Owner | akrowne (2) |

Last modified by | akrowne (2) |

Numerical id | 10 |

Author | akrowne (2) |

Entry type | Definition |

Classification | msc 40-00 |

Synonym | monotone increasing |

Synonym | strictly increasing |

Related topic | MonotonicallyDecreasing |