Definition:Minimal Element/Definition 1

Definition
Let $\struct {S, \RR}$ be a relational structure.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a minimal element (under $\RR$) of $T$ :


 * $\forall y \in T: y \mathrel \RR x \implies x = y$

That is, the only element of $T$ that $x$ succeeds or is equal to is itself.

Also see

 * Equivalence of Definitions of Minimal Element