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

(i)	\begin{equation} X \neq \emptyset \end{equation}
(ii)	$E \subseteq X$ is a D78: Subset

A D2218: Set element $a \in X$ is an upper bound of $E$ in $P$ if and only if \begin{equation} \forall \, x \in E : (x, a) \in {\preceq} \end{equation}

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

(i)	\begin{equation} X \neq \emptyset \end{equation}
(ii)	$E \subseteq X$ is a D78: Subset

A D2218: Set element $a \in X$ is an upper bound of $E$ in $P$ if and only if \begin{equation} \forall \, x \in E : x \preceq a \end{equation}

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

(i)	\begin{equation} X \neq \emptyset \end{equation}
(ii)	$E \subseteq X$ is a D78: Subset

A D2218: Set element $a \in X$ is an upper bound of $E$ in $P$ if and only if \begin{equation} E \preceq a \end{equation}