Definition:Empty Supremum

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

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

Also see

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


 * Definition:Supremum of Set
 * Definition:Empty Infimum