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*To*: jar@cs.cornell.edu*Subject*: Re: (rational? (sqrt 2))*From*: Hans_Boehm.PARC@xerox.com*Date*: Mon, 17 Feb 1992 17:13:01 PST*Cc*: Hans_Boehm.PARC@xerox.com, RRRS-Authors@mc.lcs.mit.edu*In-Reply-To*: "<9202180024.AA18321@kama.cs.cornell.edu>"*Posted-Date*: Mon, 17 Feb 92 17:03:56 PST

The problem is that all irrationals are represented inexactly as floating point numbers, which are rational. RRRs states that real? and rational? are likely to be the same. Once you represent the result of (sqrt 2) inexactly, it's unlikely that you'll be able to tell if it was rational. Even using constructive real arithmetic doesn't help, since deciding whether a constructive real is rational is undecidable. Algebraic numbers would help, I think. But my understanding is that they're too expensive to be used at that level. Hans

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