Definition:Strictly Monotone/Mapping

Definition

Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be posets.

Let $\phi: \left({S, \preceq_1}\right) \to \left({T, \preceq_2}\right)$ be a mapping.

Then $\phi$ is strictly monotone iff 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

• Increasing Mapping
• Decreasing Mapping
• Monotone Mapping

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 14$