Countable

Statement

A set $S$ is countable if there exists a Bijection $f : \mathbb{N} \to S$. If there does not exist such a Bijection then we say that $S$ is uncountable.

The Cardinality of a countable set is the same as that of the Natural Numbers, denoted $\aleph_0$.

Explanation

Proof(s)

History

Applications

Links

Dependencies

• Natural Numbers
• Cardinality
• Bijection

Dependents

• Integers are Countable

Sources

• Hrbacek, K., & Jech, T. (1999). Introduction to Set Theory, Revised and Expanded (3rd ed.). CRC Press. https://doi.org/10.1201/9781315274096