IEVref: 102-01-09 ID: Language: en Status: 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 setNote 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: