Definition:Empty Infimum

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

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

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

Also see

 * Infimum (Ordered Set)
 * Definition:Empty Supremum