partial order (original) (raw)
A total order
is a partial order that satisfies a fourth property known as comparability:
A set and a partial order on that set define a poset.
Remark. In some literature, especially those dealing with the foundations of mathematics, a partial order ≤ is defined as a transitive
irreflexive
binary relation (on a set). As a result, if a≤b, then b≰a, and therefore ≤ is antisymmetric.
| Title | partial order |
|---|---|
| Canonical name | PartialOrder |
| Date of creation | 2013-03-22 11:43:32 |
| Last modified on | 2013-03-22 11:43:32 |
| Owner | mathcam (2727) |
| Last modified by | mathcam (2727) |
| Numerical id | 24 |
| Author | mathcam (2727) |
| Entry type | Definition |
| Classification | msc 06A06 |
| Classification | msc 35C10 |
| Classification | msc 35C15 |
| Classification | msc 55-01 |
| Classification | msc 55-00 |
| Synonym | order |
| Synonym | partial ordering |
| Synonym | ordering |
| Related topic | Relation |
| Related topic | TotalOrder |
| Related topic | Poset |
| Related topic | BinarySearch |
| Related topic | SortingProblem |
| Related topic | ChainCondition |
| Related topic | PartialOrderWithChainConditionDoesNotCollapseCardinals |
| Related topic | QuasiOrder |
| Related topic | CategoryAssociatedToAPartialOrder |
| Related topic | OrderingRelation |
| Related topic | HasseDiagram |
| Related topic | NetsAndClosuresOfSubspaces |