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).]]
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Encyclopedic overview
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.
Excerpted from Wikipedia’s “preorder” article, available under the CC BY-SA 4.0 licence.