Definition:Strictly Monotone/Mapping
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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 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
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings