preorder
Sign in to savethumb|x R y defined by xinteger division|//4≤y//4 is a preorder on the [[natural numbers. It corresponds to the equivalence relation x E y defined by x//4=y//4. The set of equivalence classes is partially ordered, and thus can be shown as a Hasse diagram (depicted).]]
~14 min read
Article
18 sectionsContents
- Definition
- Preorders as partial orders on partitions
- Relationship to strict partial orders
- Strict partial order induced by a preorder
- Preorders induced by a strict partial order
- Examples
- Graph theory
- Computer science
- Category theory
- Other
- Constructions
- Related definitions
- Uses
- Number of preorders
- Interval
- See also
- Notes
- References
thumb|x R y defined by xinteger division|//4≤y//4 is a preorder on the [[natural numbers. It corresponds to the equivalence relation x E y defined by x//4=y//4. The set of equivalence classes is partially ordered, and thus can be shown as a Hasse diagram (depicted).]]
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name is meant to suggest that preorders are almost partial orders, but not quite, as they are not necessarily antisymmetric.