1 Cardinality of infinite sets Definition 1.1. Let A and B be nonempty sets. We say that the cardinality of A is equal to the cardinality of B if there exists a bijection from A to B. We denote the cardinality of A by |A|. We define the cardinality of the empty set to be zero. The cardinality of the set of natural numbers is denoted as No. If a set A has the same cardinality as that of N, we say that A is countably infinite. A countable set is either finite or countably infinite.Theorem 1.5 (Schroeder-Bernstein). If |A|