Definition:Minimal Element/Definition 1

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

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

An element $x \in T$ is a minimal element of $T$ :


 * $\forall y \in T: y \preceq x \implies x = y$

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

Also see

 * Equivalence of Definitions of Minimal Element