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From: scottb@elvis.wri.com ( )
Subject: Re: Are integers rational? Are rationals real?
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Date: Wed, 23 Aug 1995 17:14:40 GMT
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Xref: glinda.oz.cs.cmu.edu sci.physics:136331 sci.math:115331 comp.ai:32761

Patrick Juola writes:

>2.0 *is* an integer since it's identical to the
>integer 2.  That's one of the big fallacies of computer science, that
>real numbers and integers are somehow different.  Integers are simply
>a subset of the rationals, which in turn are a subset of the reals, &c.

  I missed the start of this thread, so forgive me if I'm missing
  part of the point. What you write above seems similar to a computer
  scientist asserting "That's one of the big fallacies of mathematics,
  that a constructive existence proof using an algorithm that is
  hyperexponential is just as good as one using a log-linear algorithm".

  In computer science, reals and integers *are* different. They are
  stored differently, manipulated differently, and raise different
  issues of accuracy. You can *almost* always get away with treating
  integers as floats, but rounding errors may occasionally give
  different results if two integers are manipulated as floats as
  opposed to as integers.

  Not that I disagree strongly with you, but I'd not say that what you
  describe is a "fallacy" of computer science.

  Scott


