 Definition: If A is a finite set, then \(\mathcal{S}_A = \{X \mid X \sim A \}\) is the class of all sets equinumerous with A. The associated generalization operation is the cardinality function: \(|A| =\mathcal{S}_A = \{X \mid X \sim A \} = n\). This defines a natural number \(|A|= n \in \mathbb{N}\) associated with the set A. 