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Re: My ideas about infinity in Scheme (revised)

This page is part of the web mail archives of SRFI 70 from before July 7th, 2015. The new archives for SRFI 70 contain all messages, not just those from before July 7th, 2015.

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 

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
  (= 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.]