Definition:Monotone
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Disambiguation
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Monotone may refer to:
- Mappings:
- Monotone (Order Theory): A mapping from one ordered set to another is monotone if and only if it is either increasing or decreasing.
- Monotone (Measure Theory): A mapping $f: \SS \to \R$ on an algebra of sets $\SS$ is monotone if and only if $A \subseteq B \iff \map f A \le \map f B$.
- Monotone class: A collection of subsets closed under countable intersections and unions.
In all cases, the sense is one of changing always in the same direction.
Also known as
Monotone is also seen rendered as monotonic.
Also see
- Results about monotone can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): monotonic (monotone)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): monotonic (monotone)