# Category:Definitions/Decreasing Mappings

This category contains definitions related to Decreasing Mappings.
Related results can be found in Category: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 $S = T$.

## Pages in category "Definitions/Decreasing Mappings"

The following 12 pages are in this category, out of 12 total.