Definition:Cardinal

Definition
Let $$S$$ be a set.

Associated with $$S$$ there exists a set $$\operatorname{Card} \left({S}\right)$$ called the cardinal of $$S$$.

It has the properties:
 * $$\operatorname{Card} \left({S}\right) \sim S$$, i.e. $$\operatorname{Card} \left({S}\right)$$ is (set) equivalent to $$S$$;
 * $$S \sim T \iff \operatorname{Card} \left({S}\right) = \operatorname{Card} \left({T}\right)$$.