Monotonicitynon-monotonicMonotone function exampleMonotonic decreasingMonotonically increasingMonotone function definitionMonotonic functionMonotonic signalMonotonic Function -- from Wolfram MathWorld
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A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be ... Algebra AppliedMathematics CalculusandAnalysis DiscreteMathematics FoundationsofMathematics Geometry HistoryandTerminology NumberTheory ProbabilityandStatistics RecreationalMathematics Topology AlphabeticalIndex NewinMathWorld CalculusandAnalysis Calculus IncreasingandDecreasing CalculusandAnalysis MeasureTheory CalculusandAnalysis GeneralAnalysis MathWorldContributors Stover More...Less... MonotonicFunction Amonotonicfunctionisafunctionwhichiseitherentirelynonincreasingornondecreasing.Afunctionismonotonic ifitsfirstderivative(whichneednotbecontinuous) doesnotchangesign. Thetermmonotonicmayalsobeusedtodescribesetfunctionswhichmapsubsetsofthedomain tonon-decreasingvaluesofthecodomain.Inparticular, ifisasetfunctionfromacollection ofsetstoanordered set,thenissaidtobe monotoneifwheneveraselementsof,. Thisparticulardefinitioncomesupfrequentlyinmeasure theorywheremanyofthefamiliesoffunctionsdefined(includingouter measure,premeasure,andmeasure) beginbyconsideringmonotonicsetfunctions. SeealsoCompletelyMonotonicFunction,Measure,Measure Theory,Monotone,Monotone Decreasing,MonotoneIncreasing,Nondecreasing Function,NonincreasingFunction,OuterMeasure,Premeasure ThisentrycontributedbyChristopher Stover ExplorewithWolfram|Alpha Morethingstotry: exp(x) ln(x) plottan(x)fromx=-pi/2topi/2 ReferencesRoyden,H. L.andFitzpatrick,P. M.RealAnalysis.Pearson,2010.ReferencedonWolfram|AlphaMonotonicFunction Citethisas: Stover,Christopher."MonotonicFunction."FromMathWorld--AWolframWebResource,createdbyEric W.Weisstein.https://mathworld.wolfram.com/MonotonicFunction.html Subjectclassifications CalculusandAnalysis Calculus IncreasingandDecreasing CalculusandAnalysis MeasureTheory CalculusandAnalysis GeneralAnalysis MathWorldContributors Stover More...Less... Created,developedandnurturedbyEricWeissteinatWolframResearch
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That is if x1 > x2, then f(x1) > f(x2). On the other hand, a function is called decreasing on an ...
