Definition:Strictly Decreasing/Mapping

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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 decreasing if and only if:

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

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

Also known as

A strictly decreasing mapping is also known as a strictly order-reversing mapping.

Also see

  • Results about strictly decreasing mappings can be found here.