Cardinal Number (Set Theory)

In set theory, cardinal numbers (or cardinal) are a generalisation of the natural number used to measure the cardinality (size) of sets. On the one hand, the cardinality of a finite set is a natural number. On the other hand, the transfinite cardinal numbers describe the sizes of infinite sets.

A fundamental theorem, by Georg Cantor, shows that it is possible for infinite sets to have different cardinalities. In particular, the cardinality of the set of real numbers is greater than the one of the set of natural numbers. It is also possible that a proper subset of an infinite set to have the same cardinality as the original set. This cannot happen with proper subsets of finite sets.

References

• https://en.wikipedia.org/wiki/Cardinal_number