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IEVref:102-01-09ID:
Language:enStatus: Standard
Term: order relation
Synonym1: order
[Preferred]
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Definition: binary relation ℛ between elements a and b of a given set having the following properties:

  • reflexivity: aa,
  • antisymmetry: if ab and ba then a = b,
  • transitivity: if ab and bc then ac, for any elements a, b and c of the given set

Note 1 to entry: The given set is said to be ordered by the relation ℛ.

Note 2 to entry: An order relation is a total order if at least one of the relations ab and ba is true for any elements a and b. The usual order for real numbers is a total order because ab or ba.

Note 3 to entry: An order relation is a partial order if, for at least two elements a and b, neither ab nor ba is true. Examples are the divisibility relation for natural numbers and the inclusion relation for subsets of a set with at least two elements.


Publication date:2008-08
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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