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*To*: Paul Schlie <schlie@xxxxxxxxxxx>, Aubrey Jaffer <agj@xxxxxxxxxxxx>, <srfi-70@xxxxxxxxxxxxxxxxx>*Subject*: Re: infinity notations*From*: Paul Schlie <schlie@xxxxxxxxxxx>*Date*: Mon, 04 Jul 2005 15:25:05 -0400*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <BEEEFFC8.AB77%schlie@xxxxxxxxxxx>*User-agent*: Microsoft-Entourage/11.1.0.040913

> And I'll concede my perceived necessity to denote an ambiguously signed > infinity in exchange for the prevention of incorrectly signed infinities, > which means that the region about 0 must be considered correspondingly > invalid, (i.e. both are considered NaN or 0/0). yielding: > > > / NaN \ or equivalently: / 0/0 \ > / | \ / | \ > -Inf | +Inf -1/0 | +1/0 > ------+------- (reciprocal projection axis) ------+------ > -0.0 | 0.0 -0.0 | +0.0 > \ | / \ | / > \ NaN / \ 0/0 / > | | > 0 0 > (negative projection axis) (negative projection axis) > > (where NaN and +-Inf may be thought of as symbols defined as 0/0 and +-1/0) > > Which helps eliminates the ordering concern, although it's likely still a > good idea to define (= -0.0 0 +0.0) => #t, and (< -0.0 0 +0.0) => #t, etc. > > However then 0/0 denotes all ambiguities in either sign or value, even those > which may be very small, then Therefore: > > (+ +0.0 -0.0) => 0/0 [aka NaN] > > as otherwise: > > (/ (+ +0.0 -0.0 +0.0)) :: (/ (+ 0 +0.0)) :: (/ +0.0) => +Inf > > [which would be incorrect] > > Thereby one can argue that this is actually good, as then the iterative sum > of alternating infinitely small value about 0 is considered ambiguous, which > would typically be the case. and correspondingly yield 0/0 for all > ambiguities in either sign or significant magnitude. > > (tan pi/2) => 0/0 > (/ 0.0 0.0) => 0/0 and as it may not be obvious, the difference between any two equivalently valued inexact value is an exact 0. I.e.: (- 1.5 1.5) => 0 as there is no inexact 0, as that would imply a value about 0 with an ambiguous sign, which would both have a value range which overlaps +0.0, 0, and +0.0; and who's reciprocal was not self consistent. (or if one chooses, an exact 0 is equivalent to an inexact 0, both mean absolute 0.)

**References**:**Re: infinity notations***From:*Paul Schlie

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