Definition:Strictly Monotone/Mapping
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Definition
Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.
Let $\phi: \left({S, \preceq_1}\right) \to \left({T, \preceq_2}\right)$ 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): $\S 14$