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 minimum element in $P$ if and only if \begin{equation} \forall \, x \in X : (m, x) \in {\preceq} \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 minimum element in $P$ if and only if \begin{equation} \forall \, x \in X : m \preceq x \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 minimum element in $P$ if and only if \begin{equation} m \preceq X \end{equation}