Essays on the Theory of Numbers
by Richard Dedekind
Publisher: The Open Court Publishing 1901
Number of pages: 78
This is a book combining two essays by Dedekind: "Continuity and irrational numbers" - Dedekind's way of defining the real numbers from rational numbers; and "The nature and meaning of numbers" where Dedekind offers a precise explication of the natural numbers (using what are now called the Peano axioms, since Peano made so much of them after reading Dedekind).
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by Edward Nelson - Princeton Univ Pr
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
by Charles Ashbacher - Erhus Univ Pr
In the 1970's a Rumanian mathematician Florentin Smarandache created a new function in number theory, which consequences encompass many areas of mathematics.The purpose of this text is to examine some of those consequences.
by Krassimir Atanassov - Erhus Univ Pr
A collection of 27 Smarandache's problems which the autor solved by 1999. 22 problems are related to different sequences, 4 problems are proved, modifications of two problems are formulated, and counterexamples to two of the problems are constructed.
by Wolfgang M. Schmidt - Tata Institute of Fundamental Research
The theory of Irregularities of Distribution began as a branch of Uniform Distributions, but is of independent interest. In these lectures the author restricted himself to distribution problems with a geometric interpretation.