Category:Definitions/Increasing Mappings

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This category contains definitions related to Increasing Mappings.
Related results can be found in Category:Increasing Mappings.

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

Let $\phi: S \to T$ be a mapping.

Then $\phi$ is increasing if and only if:

$\forall x, y \in S: x \preceq_1 y \ \implies \phi \left({x}\right) \preceq_2 \phi \left({y}\right)$

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

Also see