Category:Monotone Mappings

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This category contains results about Monotone Mappings.
Definitions specific to this category can be found in Definitions/Monotone Mappings.

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 $S = T$.