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

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 6$ Finite Sets