A transitive set is a set 
such that every element of 
is a subset
of 
. Equivalently, whenever 
, then 
. Every ordinal number
is a transitive set, and the set-theoretic transitive
closure is transitive by construction.
Transitive Set
See also
Ordinal Number, Subset, Transitive ClosureExplore with Wolfram|Alpha
References
Jech, T. Set Theory, 3rd millennium ed. Berlin, Germany: Springer-Verlag, 2003.Cite this as:
Weisstein, Eric W. "Transitive Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TransitiveSet.html