Definition: For nonempty sets \(A, B\), we say that the cardinality of \(A\) is no smaller than the cardinality of \(B\), and write \(|A| \geq |B|\), to mean there is an onto function with domain \(A\) and codomain \(B\). Also, we define \(|A| \geq |\emptyset|\) for all sets \(A\).