Transitive Set

Statement

A set $T$ is transitive iff $a \in T \implies a \subset T$.

Equivalently, if $a \in T$ and $b \in a$ then $b \in T$.

Explanation

Proof(s)

History

Applications

Links

Dependencies

Dependents

• Ordinal Numbers
• Natural Numbers Are Transitive
• 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