[R6RS] NaNs and infinities

[dyb at cs.indiana.edu]

> I was addressing a person who thinks integers can be infinite,
> and didn't want his beliefs to get in the way of understanding
> my point.
>
> > Does this mean that infinite integers are irrational?
>
> There are no infinite integers, in ordinary mathematical
> usage or in the current draft of SRFI 77.

Gosh.  So there really are no infinite integers and no infinite rationals?
You're blowing my mind.  Next you'll probably tell me that there are no
infinite reals either.

I'll save you the trouble in the hopes of putting an end to this foolish
banter: There are no infinite reals in ordinary mathematical usage.
So drawing the line between rational? and real? makes no sense from
a mathematical standpoint.  I say +inf.0 and -inf.0 should either be
integers (so justified because they represent the limits of a set of
numbers that become integers long before they reach +inf.0 or -inf.0)
or they shouldn't be rational?, real?, or complex?.  It's bizarre to
draw the line in so arbitrary a manner, merely to avoid mentioning how
a few primitives handle +inf.0 and -inf.0.  It's even more bizaare to do
so to make rational? useful as a predicate to test for nans and infinities
(and that only in systems that actually support irrational numbers).

Anyway, I've said my peace and will let you proceed as you see fit.

Kent