Definition:Empty Supremum

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

Then the empty supremum is the supremum $\sup \O$.

Notation
The empty supremum is sometimes denoted as $0$.

Also see

 * Supremum of Empty Set is Smallest Element: the empty supremum exists $\struct {S, \preceq}$ has a smallest element.


 * Definition:Supremum of Set
 * Definition:Empty Infimum