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.
• 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.

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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

2009b

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Partially_ordered_set
• http://www.algebra.com/algebra/homework/Inequalities/Partially_ordered_set.wikipedia

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