Definition:Strictly Decreasing/Mapping

Definition

Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be posets.

Let $\phi: \left({S, \preceq_1}\right) \to \left({T, \preceq_2}\right)$ be a mapping.

Then $\phi$ is strictly decreasing (or strictly order-reversing) if:

$\forall x, y \in S: x \prec_1 y \iff \phi \left({y}\right) \prec_2 \phi \left({x}\right)$

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

Also see

• Decreasing Mapping
• Strictly Increasing Mapping
• Strictly Monotone Mapping

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 14$