Definition:Maximal/Ordered Set/Definition 1

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Let $\struct {S, \preceq}$ be an ordered set.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a maximal element of $T$ if and only if:

$x \preceq y \implies x = y$

That is, the only element of $S$ that $x$ precedes or is equal to is itself.

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