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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 Fri, 22 Jul 2005, William D Clinger wrote:

>Suppose (for a contradiction) that inexact numbers do denote
>neighborhoods.  Then let [x, y] be the neighborhood denoted
>by the inexact number 1.0.  If 0 < x <= y, then the inexact
>number (* 1.0 1.0) denotes [x*x, y*y].  If (* 1.0 1.0)
>evaluates to 1.0, then 1.0 denotes both [x, y] and [x*x, y*y],
>hence x = x*x and y = y*y.  Therefore x = 1.0 = y, so under
>our assumptions, the inexact number 1.0 really denotes only
>itself.  (Had we considered an open neighborhood (x, y) with
>0 < x <= y, we'd have concluded that the neighborhood denoted
>by 1.0 is empty, which is even less satisfactory.)

Thank you, that's much more rigorously constructed than my
argument.  I could see that it was false in the presence of
operations with inexact arguments, but did not go through the
rigorous disproof and pick a counterexample.