The

**set of lower bounds**of $E \subseteq X$ with respect to $P$ is the D11: Set \begin{equation} \mathsf{LB}_P(E) : = \{ m \in X \mid \forall \, x \in E : (m, x) \in {\preceq} \} \end{equation}

Definition D553

Set of lower bounds

Formulation 0

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

The**set of lower bounds** of $E \subseteq X$ with respect to $P$ is the D11: Set
\begin{equation}
\mathsf{LB}_P(E) : = \{ m \in X \mid \forall \, x \in E : (m, x) \in {\preceq} \}
\end{equation}

The

Formulation 1

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

The**set of lower bounds** of $E \subseteq X$ with respect to $P$ is the D11: Set
\begin{equation}
\mathsf{LB}_P(E) : = \{ m \in X \mid \forall \, x \in E : m \preceq x \}
\end{equation}

The

Children

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