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*To*: srfi-70@xxxxxxxxxxxxxxxxx*Subject*: Re: My ideas about infinity in Scheme (revised)*From*: Ken Dickey <Ken.Dickey@xxxxxxxxxxxxxx>*Date*: Sat, 21 May 2005 06:59:46 -0700*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <20050521063128.9C70A147C@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>*Organization*: BitWize Consulting*References*: <20050521063128.9C70A147C@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>*User-agent*: KMail/1.7

On Friday 20 May 2005 23:30, Chongkai Zhu wrote: > ======= At 2005-05-21, 09:21:47 Ken Dickey wrote: ======= > > >But computational infinities are not really numbers. They are special > > markers for places where limits of the number system are exceeded. > > No. Even in a Scheme implementation that support arbitrary big number, > there can be need for infinity (just as in mathematics). But infinity in mathematics is typically used to express processes (e.g. of constructing non-finite sets) or saying "we have run out of fingers to count on". There is no such number as "infinity". That is a figment of language. One always "compares infinities" by comparing how they were constructed. How would one compare "the number of digits of pi" with "the number of odd integers"? I am sure one could construct such a theory, but I for one would not find meaning in it. Computationally, we try for elegance. But I would personally be happy with (eq? 1/0 1/0) => #t but (= 1/0 1/0) => #f or an error I think in the context of SRFI-70 (= 1/0 1/0) => #t is fine. But choosing the other interpretation/implementation would not bother me. [As you can see, I lean toward constructive mathematics.] $0.02, -KenD

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

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