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Re: inexactness vs. exactness

This page is part of the web mail archives of SRFI 70 from before July 7th, 2015. The new archives for SRFI 70 contain all messages, not just those from before July 7th, 2015.

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.