Definition:Greatest 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 greatest element of $A$ :


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

Thus for an element $x$ to be the greatest element, all $y \in S$ must be comparable to $x$.

Also see

 * Definition:Smallest Element (Class Theory)