Definition:Cardinality of Finite Class/Definition 2

Definition
Let $A$ be a class. Let $A$ be such that:
 * there exists a bijection $\phi$ from $A$ to the set $\set {1, 2, \dotsc, n} = n^+ \setminus \set 0$

where:
 * $n$ is a natural number as defined by the von Neumann construction
 * $n^+$ is the successor of $n$.

Then $A$ has cardinality $n$.

Also see

 * Equivalence of Definitions of Cardinality of Finite Class