ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D297
Set lower bound

Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that
 (i) $$X \neq \emptyset$$ (ii) $E \subseteq X$ is a D78: Subset of $X$
A D2218: Set element $a \in X$ is a lower bound of $E$ in $P$ if and only if $$\forall \, x \in E : (a, x) \in {\preceq}$$

Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that
 (i) $$X \neq \emptyset$$ (ii) $E \subseteq X$ is a D78: Subset of $X$
A D2218: Set element $a \in X$ is a lower bound of $E$ in $P$ if and only if $$\forall \, x \in E : a \preceq x$$

Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that
 (i) $$X \neq \emptyset$$ (ii) $E \subseteq X$ is a D78: Subset of $X$
A D2218: Set element $a \in X$ is a lower bound of $E$ in $P$ if and only if $$a \preceq E$$
Children
 ▶ D553: Set of lower bounds