That makes complete sense when you consider that IEEE 754 is all about approximating values, though. It is possible that the value you're trying to represent is smaller than the smallest values actually representable by IEEE 754 floating point, but it would be nice if you could at least preserve the sign information (so that, as you point out, dividing produces the correct `Inf` value).

The real WTF in IEEE 754 is why there needs to be so many different ways to represent NaN.