Difference between revisions of "Transitive set"
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Karl Jones (Talk | contribs) (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...") |
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* whenever x ∈ A, and y ∈ x, then y ∈ A, or, equivalently, | * 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. | Similarly, a class M is transitive if every element of M is a subset of M. | ||
| Line 9: | Line 9: | ||
* [[End extension]] | * [[End extension]] | ||
| + | * [[Subset]] | ||
* [[Supertransitive class]] | * [[Supertransitive class]] | ||
* [[Transitive relation]] | * [[Transitive relation]] | ||
| + | * [[Urelement]] | ||
== External links == | == External links == | ||
Latest revision as of 09:09, 17 September 2016
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 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
External links
- Transitive set @ Wikipedia.org
