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.
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.
 Only operator< is fundamental; the other inequality operators are essentially syntactic sugar.
 Antisymmetry is a theorem, not an axiom: it follows from irreflexivity and transitivity.
 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, StrictWeakOrdering
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