Category:Definitions/Monotone Mappings

This category contains definitions related to Monotone Mappings.
Related results can be found in Category: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 $S = T$.