[racket] Exact Infinity?

I've been doing some work that uses a data structure that includes a size
that can be either a Natural number of Infinity ,a so-called "extended
natural number".

I've been using +inf.0 and gotten by using `<` and `infinite?` and things
have worked fine out of the box but now I need to take the minimum of such
numbers, but

> (min 0 +inf.0)
returns 0.0, an inexact 0. This behavior is expected:
http://docs.racket-lang.org/reference/generic-numbers.html?q=inf&q=min&q=min&q=list/c&q=-%3E&q=define/contract#%28def._%28%28quote._~23~25kernel%29._min%29%29because
+inf.0 (and +inf.f) is a floating point number and thus inexact.

I need to use exact naturals throughout however, so I can write a wrapper
that takes the floor of the number after a call to min or I can define my
own min that returns the original arguments.

(define (mymin a b)
  (if (< a b) a b))

But would it be useful if exact infinities were added to the numeric tower?
I'll call them +inf and -inf. Most operations like +, * etc could be
defined easily though you would probably also want to add an "exact" nan
for say (+ +inf -inf). The operations would work exactly the same way they
do for inexact infinities, except returning exact numbers when possible, so
for example

(1 . / . +inf) ==> 0
(min 34 +inf) ==> 34

-Max Stewart New
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