A construction of the real number system from axioms for the natural numbers. The concept of isomorphic mappings plays a central role. The reals are introduced through Cauchy sequences or Dedekind cuts in the rationales, as the text may require, and either approach is used to develop various wordings of the completeness property. Special topics such as finite cardinal numbers, summation notation, decimal representation, or complex numbers are treated when time allows. Prerequisite: Successful completion of MATH 300 with a grade of C- or better. As needed.