No IEEE rationale, the standard dealing with this stuff is IEEE 754 (and its revision IEEE 754r) but it only discusses things like the bit patterns for representing those values.
I recently followed the discussion on your post How to create nan/inf with interest. In Perl 6 everything will be better, but when I read A Romp Through Infinity I was a bit puzzled/confused.
In mathematics it is well defined but outside of math it seems to depend on the specific domain, i.e. you can find thousands of papers discussing infinity/NaN on IEEE. Enjoy:-)
IEEE-754 References for the NaN/Inf inclined monk.