Total Relation

A Total Relation is a Binary Relation that is defined for all pairs in a predefined set.

• AKA: Complete Relation, Total Single Set Relation.
• Context:
  • ∀a,b ∈ S: R(a,b) ∨ R(b,a).
• Example(s):
  • the GreaterThan is a Total Strict Partial Order Relation associated to the Number Line.
  • the GreaterThanOrEqualTo is a Total Weak Partial Order Relation associated to the Number Line.
• See: Partial Relation, Total Function.

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References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Total_relation
  • In mathematics, a binary relation R over a set X is total if it holds for all a and b in X that a is related to b or b is related to a (or both).
  • In mathematical notation, this is: \forall a, b \in X,\ a R b \or b R a.

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