Function

Statement

A function $F$ is a Relation such that if $(x,y) \in F$ and $(x,z) \in F$ then $y = z$.

Explanation

Effectively, a function is a set of [Ordered Pairs|Ordered Pair] for which inputs occur only once, i.e. every input (left element) is assigned a unique output (right element).

Proof(s)

History

Applications

Links

Dependencies

• Relation

Dependents

• Bijection
• Injective Function
• Surjective Function
• Addition of Cardinals is non Decreasing
• Addition of Cardinals Preserves Ordering
• Balanced Function
• Deutsch Function
• Constant Function
• Limit of a Function
• Sequence
• Continuous Function
• Domain of a Function

Sources

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