Transitive Set

Pub Mar 01, 2026 Up Jun 08, 2026

Definition 1. A set $T$ is transitive if every element of $T$ is a subset of $T$.

Proposition 1. The following statements are equivalent:

  1. $T$ is transitive.

  2. \[\bigcup T \subseteq T.\]
  3. \[T \subseteq \powerset(T).\]