Definition:Greatest Element/Subset

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Definition

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

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


An element $x \in T$ is the greatest element of $T$ if and only if:

$\forall y \in T: y \preceq \restriction_T x$

where $\preceq \restriction_T$ denotes the restriction of $\preceq$ to $T$.


Also see


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