Definition:Cardinality of Finite Class
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Definition
Let $A$ be a class.
Definition 1
Let $A$ be such that:
- there exists a bijection $\phi$ from $A$ to $n$
where $n$ is a natural number as defined by the von Neumann construction.
Then $A$ has cardinality $n$.
Definition 2
Let $A$ be such that:
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 known as
This condition can more obviously be put as:
- $A$ has $n$ elements.