Definition:Empty Infimum

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

Then the empty infimum is the infimum $\inf \O$.

By Infimum of Empty Set is Greatest Element, it exists $\struct {S, \preceq}$ has a greatest element.

Also see

 * Definition:Infimum of Set
 * Definition:Empty Supremum