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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Preordering relation

▾ Partial ordering relation

▾ Partially ordered set

▾ Minimal element

▾ Minimum element

▾ Set lower bound

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Preordering relation

▾ Partial ordering relation

▾ Partially ordered set

▾ Minimal element

▾ Minimum element

▾ Set lower bound

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

Child definitions