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From: dik@cwi.nl (Dik T. Winter)
Subject: Re: Are integers rational?  Are rationals real?
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References: <NEWTNews.809103968.6053.richard.caldwell@oufan.oklaosf.state.ok.us> <41cq12$sar@csnews.cs.colorado.edu> <41dm5s$5if@banach.mit.edu>
Date: Tue, 22 Aug 1995 23:04:09 GMT
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Xref: glinda.oz.cs.cmu.edu sci.physics:136135 sci.math:115225 comp.ai:32702

In article <41dm5s$5if@banach.mit.edu> baez@math.mit.edu (John Baez) writes:
 > In article <41cq12$sar@csnews.cs.colorado.edu>,
 > Patrick Juola <juola@suod.cs.colorado.edu> wrote:
 > >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.
...
 > And this is related to "type conversion" in computer science, if
 > I have my jargon straight.  With a computer, you actually have to
 > do a bit of work to turn the integer 2 into the real 2.  (Here,
 > by "real", I guess I really mean something like a floating point
 > number... the computer doesn't have room for ALL real numbers, so
 > one picks a nice big subset of them and hopes that's good enough.)

Indeed, the analogy is a bit wrong.  In computerese the "reals" are
(mostly) floating point numbers and those in turn are a subset of
the rationals.  And indeed, you have work to do to turn an integer
in a floating point number for most representations of fp numbers;
if it can be done at all (the integers do not necessarily form a
"subset" of the floating point numbers).
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924098
home: bovenover 215, 1025 jn  amsterdam, nederland; e-mail: dik@cwi.nl
