# Rational Infinity

```Re:                        . . .   Since rational arithmetic doesn't
overflow, associating rational infinities with IEEE infinities would
confuse the distinction between the two IEEE uses of infinity.
The only connection I saw for "IEEE" was that it provided both negative
and positive infinities.  Dan Hoey has provided the best reasoning I've
seen so far for subscribing to an affine system; and Larry Masinter made
a good case for wanting to separate out the infinity representation

Re:                                     The user [can] explicitly coerce
floating-point numbers to rational, and it could just be an error to
coerce an infinity to rational.  [That's what we do at Symbolics.]
. . .
2.  You [may[ want something to do when the user attempts to coerce
a floating infinity to rational, other than signal an error.
That's a sticky point -- floating infinities do show up under "normal"
circumstances, but Nan's don't.  Providing a reasonable rational
representation for the floating infinities is a necessity when
converting back and forth.

One can carry the similarities too far; I certainly don't want to hear
about the inability to represent negative and positive fixnum zeros (even
though IEEE format has them).  Long Live twos's-complement arithmetic!

-- JonL --

```