Definition:Strictly Monotone/Mapping

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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 if and only if 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