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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
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
[As you can see, I lean toward constructive mathematics.]