Definition:Maximal Element/Definition 2

Definition
Let $\struct {S, \RR}$ be a relational structure.

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

An element $x \in T$ is a maximal element (under $\RR$) of $T$ :
 * $\neg \exists y \in T: x \mathrel {\RR^\ne} y$

where $x \mathrel {\RR^\ne} y$ denotes that $x \mathrel \RR y$ but $x \ne y$.

Also see

 * Equivalence of Definitions of Maximal Element