Definition:Smallest Element/Class Theory

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be an ordering.

Let $A$ be a subclass of the field of $\RR$.

An element $x \in A$ is the smallest element of $A$ :


 * $\forall y \in A: x \mathrel \RR y$

The smallest element of $A$ is denoted $\min A$.

Also see

 * Definition:Greatest Element (Class Theory)