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*To*: William D Clinger <will@xxxxxxxxxxx>*Subject*: Re: inexactness vs. exactness*From*: bear <bear@xxxxxxxxx>*Date*: Fri, 22 Jul 2005 15:02:12 -0700 (PDT)*Cc*: srfi-70@xxxxxxxxxxxxxxxxx, agj@xxxxxxxxxxxx*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <E1Dw5Su-000344-GF@xxxxxxxxxxxxxxxxx>*References*: <E1Dw5Su-000344-GF@xxxxxxxxxxxxxxxxx>

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. Bear

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