Contributions to the founding of the theory of transfinite numbers
By: Translated, and provided with an introd. and notes, by Philip E. B. Jourdain.
Publisher: Dover Publications
Published: 1952
Place of publication: New York
Language: eng
Number of pages: 211
Subjects: Set theory.
Other titles: Transfinite numbers.
Description: One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc., as well as in the entire field of modern logic. It is rare that a theory of such fundamental mathematical importance is expressed so simply and clearly: the reader with a good grasp of college mathematics will be able to understand most of the basic ideas and many of the proofs. Cantor first develops the elementary definitions and operations of cardinal and ordinal numbers and analyzes the concepts of "cardinality" and "ordinality." He covers such topics as the addition, multiplication, and exponentiation of cardinal numbers, the ordinal types of simply ordered aggretates, operations on ordinal types, the ordinal types of the linear continuum, and others. He then develops a theory of well-ordered aggregates, and investigates the ordinal numbers of well-ordered aggregates and the properties and extent of the transfinite ordinal numbers. -- from back cover.
Notes: Translation of two memoirs which appeared in the Mathematische Annalen for 1896 and 1897 under the title: "Beiträge sur Begründung der transfiniten Mengeniehrs."