Definition:Monotone (Order Theory)/Mapping
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Definition
Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.
Let $\phi: \struct {S, \preceq_1} \to \struct {T, \preceq_2}$ be a mapping.
Then $\phi$ is monotone if and only if it is either increasing or decreasing.
Note that this definition also holds if $S = T$.
Also defined as
Some authors take monotone mapping to mean what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called an increasing mapping.
Also known as
Some sources use the term monotonic.
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.4.3$