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Re: inexactness vs. exactness

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.