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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