| From: "Marcin 'Qrczak' Kowalczyk" <xxxxxx@knm.org.pl>
 | Date: Sat, 22 Oct 2005 20:52:50 +0200
 |
 | Aubrey Jaffer <xxxxxx@alum.mit.edu> 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?