The Continuum and Other Types of Serial Order

This classic of mathematics presents the best systematic elementary account of the modern theory of the continuum as a type of serial order -- a theory that underlies the definition of irrational numbers and makes possible a rigorous treatment of the real number system of algebra. Based on the Dedekind-Cantor ordinal theory, this text requires no knowledge of higher mathematics; an acquaintance with the natural numbers and the basics of elementary geometry are sufficient background. Contents include a historical introduction and chapters on classes in general; simply ordered classes, or series; discrete series, especially the type of the natural numbers; dense series, especially the type of the rational numbers; continuous series, especially the type of the real numbers; continuous series of more than one dimension, with a note on multiply ordered classes; and well ordered series, with an introduction to Cantor's transfinite numbers. Each definition features numerous examples, and bibliographic references throughout the text offer a critical introduction to further research.