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Re: +nan.0 problems
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.
> 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.