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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: comparison operators and *typos*From*: Paul Schlie <schlie@xxxxxxxxxxx>*Date*: Wed, 06 Jul 2005 13:55:40 -0400*Cc*: <srfi-70@xxxxxxxxxxxxxxxxx>*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*User-agent*: Microsoft-Entourage/11.1.0.040913

As one last thought: If the default value of a function were defined as the average value of it's limits, then it may be reasonable to define a number system like: -1.0 -10. -1/0 +1/0 +10. +1.0 -1.0 -10. -Inf Inf 10. 1.0 -------------- 0 -------------- :: -------------- 0 ----------- -1.0 -0.1 -0/1 +0/1 +0.1 +1.0 -1.0 -0.1 -0.0 0.0 0.1 1.0 Where absolute zero is designated as 0, and who's reciprocal is 0, as the average value of it's -1/0 and +1/0 limits would be 0; as would 0/0, and the difference of any two equivalent values, thereby eliminating the otherwise complexity and arguably negligible value of an inexact 0. i.e.: (= -0.0 0 +0.0) => #t, (< -0.0 0 +0.0) => #t, and (< -1/0 0 +1/0) => #t Thereby all functions will be legitimately valued at all points with no need of ambiguous value representation, however who's value may be more precisely determined at a specific limit through the use of a limit macro as desired. Thereby hypothetically: (presuming sufficient numerical precision) (tan pi/2) => 0 (limit (lambda (x) (tan x)) (pi/2 -0/1)) => +1/0 (limit (lambda (x) (tan x)) (pi/2 +0/1)) => -1/0 (+ 4. (/ (abs 0) 0)) => 4.0 (limit (lambda (x) (+ 4. (/ (abs x) x))) (0 -0/1)) => 3.0 (limit (lambda (x) (+ 4. (/ (abs x) x))) (0 +0/1)) => 5.0 [where I suspect if desired, any function returning a 0 resulting from an average of it's limits may optionally signal an exception, although should not likely do so by default, as it's not likely as arithmetically useful in general as returning it's limit's average value would be.]

**Follow-Ups**:**Re: comparison operators and *typos***From:*Aubrey Jaffer

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