Definition:Smallest Element/Subset

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 the smallest element of $T$ :


 * $\forall y \in T: x \mathop{\preceq \restriction_T} y$

where $\preceq \restriction_T$ denotes the restriction of $S$ to $T$.

Also see

 * Smallest Element is Unique