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# Re: +nan.0 problems

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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?

```