Transitive Relation - kipawaa/Proof-Tree GitHub Wiki

Statement

A Relation $R$ is transitive in a set $A$ iff $(a, b) \in R, (b, c) \in R \implies (a, c) \in R$ for all $a, b, c \in A$.

Explanation

Proof(s)

History

Applications

Links

Dependencies

• Relation

Dependents

• Equivalence Relation
• Partial Ordering
• Strict Ordering
• Ordinals Are Closed Under Succession

Sources

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