 The real number system formula_5 can be defined axiomatically up to an isomorphism, which is described hereafter.There are also many ways to construct "the" real number system, for example, starting from natural numbers, then defining rational numbers algebraically, and finally defining real numbers as equivalence classes of their Cauchy sequences or as Dedekind cuts, which are certain subsets of rational numbers.Another possibility is to start from some rigorous axiomatization of Euclidean geometry (Hilbert, Tarski, etc.)