The purpose on this paper is to incorporate in textbook form, notes and methods that the author has used for the past three years on an experimental basis. Set terminology is introduced and applied to the development of the number system through the set of real numbers. Rigorous proofs are used in developing the arithmetic of the various sets of numbers. Methods for solving equations and inequalities are discussed in set terminology. Graphs of solution sets of equations and inequalities are displayed, and the methods of plotting solution sets are discussed. Conclusions concerning the success of applying the material submitted in this thesis are presented in the form of observations that the writer has made during his experimentation with the material in the classroom
