monotonicity

Aliases
  • monotonicity
  • monotonic
  • monotonic function
  • monotone
  • monotone function
  • monotonically
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Austin GatlinLinkedInGitHubMastodonX
October 12, 2022 (last updated September 23, 2023)

https://en.wikipedia.org/wiki/Monotonic_function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

In calculus, a function defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing. That is... a function that increases monotonically does not exclusively have to increase, it simply must not decrease.

A function is monotonically increasing if, for all and such that , . Similar for monotonically decreasing with .

Terminology can be loose due to the fact that and can both be used. You could call one weakly monotone and the other strictly montone, but in general is to be assumed.