The static member function "min" has a defect. The function "denorm_min" returns the smallest positive value that can be represented (denormalized or not), and is implemented only for floating types. The function "lowest," new to C++11, returns the regular (i.e. not Infinity or NaN, etc.) value closest to negative-infinity. Lowest was introduced because for C++98/03, "min" returned "denorm_min" for the built-in floating types and "lowest" for built-in integer types! You can't get generic code out of that (without checking some more flags from numeric_limits).
Which version of "min" should boost::rational take? I was think of "denorm_min," since I'll be implementing that. The built-in integer types use "lowest" for "min," but don't define the other one at all.
I would treat it as a variant of the integer types, and set min() to the most negative value, and max() to the most positive value. I suppose denorm_min could be the smallest positive value, but I don't think there's any prior art for that. HTH, John.