This book introduces the reader to the author's theory of the arithmetic properties of a class of numerical functions, which is the first in an infinite sequence of such classes, which the author labels 'numerical functions'. These functions can be employed to describe many phenomena in arithmetic. The author sets out the development of this theory with the aim of showing that the postulates and processes of arithmetic admit of a multiplicity of interpretation. After developing the general theory, the author concludes by examining its properties and applications. Scholars with a background in arithmetic will find the novel perspective on the subject inspiring.

About the Author:

Eric Temple Bell was born in 1883 in Aberdeen, Scotland. His early education was obtained in England. Coming to the United States in 1902, he entered Stanford University and took his A.B. degree in 1904. In 1908 he was teaching fellow at the University of Washington, where he took his A.M. degree in 1909. In 1911 he entered Columbia University, where he took his Ph.D. degree in 1912. He returned to the University of Washington as instructor in mathematics and became full professor in 1921. During the summers of 1924-28 he taught at the University of Chicago, and in 1926 (first half) at Harvard University, when he was appointed Professor of Mathematics at the California Institute of Technology.

Dr. Bell was a former President of the Mathematical Association of America, a former Vice President of the American Mathematical Society and of the American Association for the Advancement of Science. He was on the editorial staffs of the "Transactions of the American Mathematical Society," the "American Journal of Mathematics," and the "Journal of the Philosophy of Science." He belonged to The American Mathematical Society, the Mathematical Association of America, the Circolo Matematico di Palermo, the Calcutta Mathematical Society, Sigma Xi, and Phi Beta Kappa, and was a member of the National Academy of Sciences of the United States. He won the Bocher Prize of the American Mathematical Society for his research work. His twelve published books include "The Purple Sapphire" (1924), "Algebraic Arithmetic" (1927), "Debunking Science," and "Queen of the Sciences" (1931), "Numerology" (1933), and "The Search for Truth" (1934).

Dr. Bell died in December 1960, just before the publication ofhis latest book, "The Last Problem."

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