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LessThan Comparable
DescriptionA type is LessThanComparable if it is ordered: it must be possible to compare two objects of that type using operator<, and operator< must be a partial ordering.Refinement ofAssociated typesNotation
DefinitionsConsider the relation !(x < y) && !(y < x). If this relation is transitive (that is, if !(x < y) && !(y < x) && !(y < z) && !(z < y) implies !(x < z) && !(z < x)), then it satisfies the mathematical definition of an equivalence relation. In this case, operator< is a strict weak ordering.If operator< is a strict weak ordering, and if each equivalence class has only a single element, then operator< is a total ordering. Valid expressions
Expression semantics
Complexity guaranteesInvariants
Models
Notes[1] Only operator< is fundamental; the other inequality operators are essentially syntactic sugar. [2] Antisymmetry is a theorem, not an axiom: it follows from irreflexivity and transitivity. [3] Because of irreflexivity and transitivity, operator< always satisfies the definition of a partial ordering. The definition of a strict weak ordering is stricter, and the definition of a total ordering is stricter still. See alsoEqualityComparable, StrictWeakOrderingCopyright © 1999 Silicon Graphics, Inc. All Rights Reserved. TrademarkInformation
