Category:Greatest Elements

This category contains results about Greatest Elements.
Definitions specific to this category can be found in Definitions/Greatest Elements.

Let $\struct {S, \preceq}$ be an ordered set.

An element $x \in S$ is the greatest element (of $S$) if and only if:

$\forall y \in S: y \preceq x$

That is, every element of $S$ precedes, or is equal to, $x$.

The Greatest Element is Unique, so calling it the greatest element is justified.

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