One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through problem situations and explanatory materials. The systems of whole numbers, integers, rational numbers, and real numbers are considered as algebraic systems, constructed from the axiomatically defined whole numbers. Order properties, completeness, and (infinite) cardinality are studied. The complex number field is introduced. (SD)