# Category:Definitions/Decreasing Mappings

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This category contains definitions related to Decreasing Mappings.

Related results can be found in Category:Decreasing Mappings.

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 **decreasing** if and only if:

- $\forall x, y \in S: x \preceq_1 y \implies \map \phi y \preceq_2 \map \phi x$

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

## Also see

## Pages in category "Definitions/Decreasing Mappings"

The following 17 pages are in this category, out of 17 total.

### D

- Definition:Decreasing
- Definition:Decreasing Function
- Definition:Decreasing Mapping
- Definition:Decreasing Real Function
- Definition:Decreasing Sequence
- Definition:Decreasing Sequence/Also known as
- Definition:Decreasing/Mapping
- Definition:Decreasing/Real Function
- Definition:Decreasing/Sequence
- Definition:Decreasing/Sequence/Real Sequence