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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: inexactness vs. exactness*From*: bear <bear@xxxxxxxxx>*Date*: Wed, 27 Jul 2005 09:27:05 -0700 (PDT)*Cc*: will@xxxxxxxxxxx, srfi-70@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <20050726042944.6E98F1B77B4@xxxxxxxxxxxxxxxx>*References*: <E1Dx76h-0003SE-S1@xxxxxxxxxxxxxxxxx> <20050726042944.6E98F1B77B4@xxxxxxxxxxxxxxxx>

On Tue, 26 Jul 2005, Aubrey Jaffer wrote: > So, does R5RS permit an inexact number which only one mathematical > number rounds to? R5RS certainly permits it, but it is difficult to imagine a practical implementation in which it were true. One possible such implementation (albeit not very practical) would be a system that represented numbers as promises; with the numbers as written in the source code at the leaves of an expression tree, there would be an inexact result for every exact number; but the exact numbers would look like formulas, and the inexact numbers could be calculated (to an arbitrary desired precision) from them on demand. One reason such a system wouldn't be very practical is that you'd have to define = in such a way as to ignore differences below some epsilon; otherwise a comparison of two exact equal numbers could be nonterminating because otherwise = would keep asking for approximations with more and more precision to compare as long as it hadn't yet found a difference. Another is that the phyiscal memory of the machine would still place a limit on the available precision. Bear

**Follow-Ups**:**Re: inexactness vs. exactness***From:*Paul Schlie

**References**:**Re: inexactness vs. exactness***From:*Aubrey Jaffer

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