The missing property is that every bounded set has a least upper bounds or that every cauchy sequence converges. A consequence is that you can divide the ratio

The missing property is that every bounded set has a least upper bounds or that every cauchy sequence converges. A consequence is that you can divide the rationals cleanly into disconnected parts. For example A = the set of rationals < sqrt(2) and B = the set of rationals > sqrt(2) https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers https://en.wikipedia.org/wiki/Completeness_of_the_real_numbe...