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Aubrey Jaffer <agj@xxxxxxxxxxxx> writes: > | From: "Marcin 'Qrczak' Kowalczyk" <qrczak@xxxxxxxxxx> > | Date: Sat, 22 Oct 2005 20:52:50 +0200 > | > | Aubrey Jaffer <agj@xxxxxxxxxxxx> writes: > | > | > The total order of the reals is a crucial property for many > | > applications. > | > | It is well known that the default order on the floating point > | approximation of reals is not total. > > From Wikipedia, the free encyclopedia. > <http://en.wikipedia.org/wiki/Total_order> > > In mathematics, a total order, linear order or simple order on a set > X is any binary relation on X that is antisymmetric, transitive, and > total. This means that, if we denote the relation by <=, the > following statements hold for all a, b and c in X: > > if a <= b and b <= a then a = b (antisymmetry) > if a <= b and b <= c then a <= c (transitivity) > a <= b or b <= a (totalness) > > Which condition does it violate? Totalness (as Marcin said). NaN comparisons (other than not-equals) always evaluate false. Thomas