Category:Strictly Increasing Mappings

This category contains results about Strictly Increasing Mappings.
Definitions specific to this category can be found in Definitions/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 $S = T$.