Ordered set
Encyclopedia : O : OR : ORD : Ordered set
Ordered set is used with distinct meanings in order theory
- A set with a binary relation R on its elements that is reflexive (for all a in the set aRa), antisymmetric (if aRb and bRa then a=b) and transitive (if aRb and bRc then aRc) is described as a partially ordered set or poset.
- If the binary relation is antisymmetric, transitive and also total (for all a and b in the set, aRb or bRa) then the set is a totally ordered set.
- If every non-empty subset has a least element then the set is a well-ordered set.
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.
