Distance between two sets
= Distance between two sets
{title2=$d(A,B)=\inf_{a\in A,b\in B}d(a,b)$}
= Set distance
{synonym}
The set distance is the infimum of pairwise <metric> distances. Two nonempty disjoint <compact sets> have positive set distance: continuity attains the minimum on their <Cartesian product>, and a zero minimum would give a common point. Disjoint closed sets without compactness need not have positive separation.