Injective Function - kipawaa/Proof-Tree GitHub Wiki

Statement

A Function $f : A \to B$ is injective iff for every $a, a' \in A$ we have that $f(a) = f(a') \implies a = a'$.

Explanation

This means that each element in the Domain gets mapped to a unique element in the Range.

Proof(s)

History

Applications

Links

Dependencies

• Function
• Domain of a Relation
• Range of a Relation

Dependents

• Bijection
• Ordering of Cardinal Numbers
• Addition of Cardinals is non Decreasing
• Addition of Cardinals Preserves Ordering

Sources

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