Definition:Empty Supremum

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

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

By Supremum of Empty Set is Smallest Element, it exists iff $\left({S, \preceq}\right)$ has a smallest element.

Also see

 * Supremum (Ordered Set)
 * Definition:Empty Infimum