# Weak Order Relation

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