IEVref:102-01-09ID:
Language:enStatus: Standard
Term: order relation
Synonym1: order
[Preferred]
Synonym2:
Synonym3:
Symbol:
Definition: binary relation ℛ between elements a and b of a given set having the following properties:

  • reflexivity: aℛa,

  • antisymmetry: if aℛb and bℛa then a = b,

  • transitivity: if aℛb and bℛc then aℛc, 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 aℛb and bℛa is true for any elements a and b. The usual order for real numbers is a total order because a ≤ b or b ≤ a.

Note 3 to entry: An order relation is a partial order if, for at least two elements a and b, neither aℛb nor bℛa 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
Source
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5: