Editing Monotonic function (section)

{{Short description|Order-preserving mathematical function}}
{{redirect|Monotonicity|information on monotonicity as it pertains to [[voting systems]]|monotonicity criterion|information on monotonicity as it pertains to logical systems|Monotonicity of entailment}}
{{Redirect|Monotonic|other uses|Monotone (disambiguation)}}

[[Image:Monotonicity example1.svg|right|thumb|Figure 1. A monotonically non-decreasing function]]
[[Image:Monotonicity example2.svg|right|thumb|Figure 2. A monotonically non-increasing function]]
[[Image:Monotonicity example3.svg|right|thumb|Figure 3. A function that is ''not'' monotonic]]

In [[mathematics]], a '''monotonic function''' (or '''monotone function''') is a [[function (mathematics)|function]] between [[List of order structures in mathematics|ordered sets]] that preserves or reverses the given [[order relation|order]].<ref>{{Cite book|title=Oxford Concise Dictionary of Mathematics|last1=Clapham|first1=Christopher|last2=Nicholson|first2=James|publisher=Oxford University Press|year=2014|edition=5th}}</ref><ref name=":1">{{Cite web|url=http://mathworld.wolfram.com/MonotonicFunction.html|title=Monotonic Function|last=Stover|first=Christopher|website=Wolfram MathWorld|language=en|access-date=2018-01-29}}</ref><ref name=":0">{{Cite web|url=https://www.encyclopediaofmath.org/index.php/Monotone_function|title=Monotone function|website=Encyclopedia of Mathematics|language=en|access-date=2018-01-29}}</ref> This concept first arose in [[calculus]], and was later generalized to the more abstract setting of [[order theory]].