Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that

(i)	$X \neq \emptyset$

A D2218: Set element $m \in X$ is a maximal element in $P$ if and only if \begin{equation} \forall \, x \in X \left( x \neq m \quad \implies \quad (m, x) \not\in {\preceq} \right) \end{equation}

Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that

(i)	$X \neq \emptyset$

A D2218: Set element $m \in X$ is a maximal element in $P$ if and only if \begin{equation} \forall \, x \in X \left( x \neq m \quad \implies \quad m \not\preceq x \right) \end{equation}