On Thursday 19 May 2005 19:28, Chongkai Zhu wrote:
> 1. We need both exact (rational) infinity and inexact infinity, that is,
> four special numbers:
>
> 1/0 -1/0 +inf.0 -inf.0
>
> The first two are rational and thus exact.

But computational infinities are not really numbers.  They are special markers
for places where limits of the number system are exceeded.  Being outside the
system, they can't be exact.  It is like talking about the duration of events
outside of space/time.  There is no symmetry.

We speak of 1/0, 0/0, -1/0 as numbers in the same way we speak of '() as the
end of a list or #!eof as the end of a file.  They are singleton limit
markers with no value but for computational tests.

BTW, as markers I would expect
 (eq? 1/0 1/0) -> #t

Cheers,
-KenD