Karl Jones at 16:09, 17 September 2016

2016-09-17T16:09:06Z

Karl Jones: Created page with "In set theory, a set A is '''transitive''', if and only if * whenever x ∈ A, and y ∈ x, then y ∈ A, or, equivalently, * whenever x ∈ A, and..."

2016-09-17T16:07:57Z

Created page with "In set theory, a set A is '''transitive''', if and only if * whenever x ∈ A, and y ∈ x, then y ∈ A, or, equivalently, * whenever x ∈ A, and..."

New page

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]]

@@ Line 2: / Line 2: @@
 * 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.
+* 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.
@@ Line 9: / Line 9: @@
 * [[End extension]]
 * [[Supertransitive class]]
 * [[Transitive relation]]
 == External links ==

Transitive set - Revision history

Karl Jones at 16:09, 17 September 2016

Karl Jones: Created page with "In set theory, a set A is '''transitive''', if and only if * whenever x ∈ A, and y ∈ x, then y ∈ A, or, equivalently, * whenever x ∈ A, and..."