Cardinality
The cardinality of a finite set is a natural number. The smallest cardinality is 0. The empty set has cardinality 0. If the cardinality of the set A is n, then there is a "next larger" set with cardinality n+1 (for example, the set A ∪ {A}). If ||A|| ≤ ||B|| ≤ ||A ∪ {A}||, then either ||B|| = ||A|| or ||B|| = ||A ∪ {A}||.) There is no largest finite cardinality.