Cardinal Numbers - kipawaa/Proof-Tree GitHub Wiki

Statement

A number $\kappa$ is a cardinal number if it represents the Cardinality of a set, i.e. $\kappa = \lvert A \rvert$.

We typically take representatives of cardinality from the Natural Numbers for finite sets, with $\aleph_0$ for the cardinality of the Natural Numbers and countable sets, $\aleph_1$ for the Real Numbers, etc.

Explanation

Proof(s)

History

Applications

Links

Dependencies

• Cardinality
• Natural Numbers
• Real Numbers

Dependents

• Multiplication of Cardinal Numbers
• Addition of Cardinal Numbers
• Equality of Cardinal Numbers
• Ordering of Cardinal Numbers
• Addition of Cardinals is non Decreasing
• Exponentiation of Cardinal Numbers
• Equality of Cardinal Numbers is Reflexive

Sources

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