Weak Order Relation
(Redirected from Weak Partial Order Relation)
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A Weak Order Relation is a Transitive Antisymmetric Reflexive Binary Relation.
- AKA: Weak Partial Ordering.
- Context:
- It can be:
- a Total Weak Order Relation if it is a Total Relation.
- a Non-Total Weak Order Relation if it is a Non-Total Relation.
- It can define a Partially Ordered Set.
- It can be:
- Example(s):
- GreaterThanOrEqualTo Relation, (which is also a Total Relation).
- …
- Counter-Example(s):
- GreaterThan Relation, a Strict Partial Order Relation.
- a Partial Order Relation that is not a ... relation.
- a Preorder Relation that is not a ... relation.
- See: Strict Order Relation, Hasse Diagram.
References
2009a
- (Wiktionary, 2009a) ⇒ http://en.wiktionary.org/wiki/partial_order
- Noun
- 1. (set theory) A relation that is reflexive, antisymmetric, and transitive.
- Synonym: partial ordering relation
- Related terms
- order,
- partially ordered set
- Noun
2009b
- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Partially_ordered_set
- http://www.algebra.com/algebra/homework/Inequalities/Partially_ordered_set.wikipedia