This set is the unique   complete Archimedian  eld, as well as the unique Dedekind-complete ordered  eld.
Tarski constructed an elegant second-order axiomatization of this structure. Adding two improper elements to this set gives its a nely extended version, while adding one gives its projectively extended version, which can be repre- sented by a cross-section of the Riemannian sphere. This set is the unique   complete Archimedian  eld, as well as the unique Dedekind-complete ordered  eld. This set's elements can be expressed as the limits of sequences of ratio- nal numbers. For ten points, identify this set of numbers represented with a double-struck R.
Tarski constructed an elegant second-order axiomatization of this structure.
real numbers