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*To*: srfi-70@xxxxxxxxxxxxxxxxx*Subject*: Re: My ideas about infinity in Scheme (revised)*From*: Alef Null Petrofsky <al@xxxxxxxxxxxxx>*Date*: Sat, 21 May 2005 14:39:59 -0700*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <20050521191440.B6AAB1B77B4@xxxxxxxxxxxxxxxx> (message from Aubrey Jaffer on Sat, 21 May 2005 15:14:40 -0400 (EDT))*References*: <20050520022827.D9E0C134@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> <20050521191440.B6AAB1B77B4@xxxxxxxxxxxxxxxx>

> | From: "Chongkai Zhu" <mathematica@xxxxxxxxx> > | I have also considered infinities in Scheme and have some > | different ideas: > | > | 1. We need both exact (rational) infinity and inexact infinity, > | that is, four special numbers: > | > | 1/0 -1/0 +inf.0 -inf.0 > From: Aubrey Jaffer <agj@xxxxxxxxxxxx> > How about "1/0." and "-1/0."? > | For the same reason, the syntax of "indeterminate" should be > | "0/0" (exact) and "nan.0" (inexact). The names +inf.0, -inf.0 > | and nan.0 were borrowed from PLT scheme. > > While the number syntax of R5RS can be readily extended to include > +inf.0, -inf.0 (because of the leading sign). "nan.0" runs afoul of > R5RS 2.1 Something I'd just like to throw out there is that one can represent the inexact floating-point entities "NaN" and positive and negative "infinity" without extending the r5rs BNF at all, by using #i0/0, #i1/0, and #i-1/0. (I implemented this for kawa back in 1998, but I don't know whether kawa still uses that notation.) I'm dubious about exact infinities (and I'm especially confused by the idea of Exactly Not A Number, and whether that's the same as Not Exactly A Number, or if Not Exactly A Number is what NaN has always meant and therefore the two NaNs would be Inexactly Not Exactly A Number and Exactly Not Exactly A Number), but I do acknowledge that exact infinity would make the following behavior implementable and it would make some sense: (let ((never-ending-story (list "and then, "))) (set-cdr! never-ending-story never-ending-story) (length never-ending-story)) => 1/0 [exactly] -al P.S. In r5rs, there are many different notations for exact zero: 0 -00/42 #e+.0s7i #x0@a ... et cetera. If we add the quantity Exactly Not Exactly A Number, does that mean I could start winning friends and influencing people by using 0@0/0 too?

**Follow-Ups**:**Re: My ideas about infinity in Scheme (revised)***From:*Aubrey Jaffer

**References**:**My ideas about infinity in Scheme (revised)***From:*Chongkai Zhu

**Re: My ideas about infinity in Scheme (revised)***From:*Aubrey Jaffer

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