Definition:Strictly Monotone/Mapping

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 strictly monotone it is either strictly increasing or strictly decreasing.

Note that this definition also holds if $S = T$.

Also known as
This can also be called strictly monotonic.

Also see

 * Definition:Increasing Mapping
 * Definition:Decreasing Mapping
 * Definition:Monotone Mapping