# Category:Decreasing Mappings

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This category contains results about Decreasing Mappings.

Definitions specific to this category can be found in Definitions/Decreasing Mappings.

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 **decreasing** if and only if:

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

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

## Also see

## Pages in category "Decreasing Mappings"

The following 2 pages are in this category, out of 2 total.