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> | 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?