View source for Transitive set

In [[set theory]], a [[Set (mathematics)|set]] A is '''transitive''', if and only if

* whenever x ∈ A, and y ∈ x, then y ∈ A, or, equivalently,
* whenever x ∈ A, and x is not an urelement, then x is a subset of A.

Similarly, a class M is transitive if every element of M is a subset of M.

== See also ==

* [[End extension]]
* [[Supertransitive class]]
* [[Transitive relation]]

== External links ==

* [https://en.wikipedia.org/wiki/Transitive_set Transitive set] @ Wikipedia.org 


[[Category:Mathematics]]
[[Category:Set theory]]