# Category:Definitions/Strictly Increasing Mappings

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This category contains definitions related to Strictly Increasing Mappings.

Related results can be found in **Category:Strictly Increasing 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 **strictly increasing** if and only if:

- $\forall x, y \in S: x \prec_1 y \implies \map \phi x \prec_2 \map \phi y$

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

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Strictly Increasing Mappings"

The following 4 pages are in this category, out of 4 total.