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