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Re: My ideas about infinity in Scheme (revised)



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