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| 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?