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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: +nan.0 problems*From*: Thomas Bushnell BSG <tb@xxxxxxxxxx>*Date*: Sat, 22 Oct 2005 17:51:06 -0700*Cc*: qrczak@xxxxxxxxxx, srfi-77@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*In-reply-to*: <20051022233336.236AC1B77BB@xxxxxxxxxxxxxxxxxxxxx> (Aubrey Jaffer's message of "Sat, 22 Oct 2005 19:33:36 -0400 (EDT)")*References*: <20051021145326.816C11B77BB@xxxxxxxxxxxxxxxxxxxxx> <20051021155906.GC16464@NYCMJCOWA2> <Pine.LNX.4.58.0510210910130.18969@xxxxxxxxxxxxxx> <20051022020312.GB5632@NYCMJCOWA2> <20051022163037.D2AFB1B77BB@xxxxxxxxxxxxxxxxxxxxx> <87zmp1tmd9.fsf@xxxxxxxxxxxxx> <20051022233336.236AC1B77BB@xxxxxxxxxxxxxxxxxxxxx>*User-agent*: Gnus/5.110004 (No Gnus v0.4) Emacs/21.4 (gnu/linux)

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

**Follow-Ups**:**Re: +nan.0 problems***From:*Aubrey Jaffer

**References**:**arithmetic issues***From:*Aubrey Jaffer

**Re: arithmetic issues***From:*John.Cowan

**Re: arithmetic issues***From:*bear

**Re: arithmetic issues***From:*John.Cowan

**+nan.0 problems***From:*Aubrey Jaffer

**Re: +nan.0 problems***From:*Marcin 'Qrczak' Kowalczyk

**Re: +nan.0 problems***From:*Aubrey Jaffer

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