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Essays on the Theory of Numbers (Classic Reprint): I. Continuity and Irrational Numbers, II. The Nature and Meaning of Numbers: I. Continuity and ... and Meaning of Numbers (Classic Reprint) - Softcover
Synopsis
Discover how counting and arithmetic shape the real numbers and the foundations of analysis.
This edition presents Dedekind’s influential exploration of how the simplest act—counting—leads to the whole structure of rational and real numbers. It weaves together intuitive ideas with a rigorous arithmetic grounding, explaining what it means for numbers to be continuous and how irrational numbers arise from the limits of counting processes. The work frames a path from finite arithmetic to the infinite and complete real number system.
- How counting builds the infinite series of positive integers and underpins all of arithmetic
- The concept of completeness and the distinction between rational and real numbers
- Plain, step-by-step development of continuity and its role in analysis
- The idea of transforming and comparing number systems to understand infinity
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Excerpt from Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II. The Nature and Meaning of Numbers
The development of the arithmetic of rational numbers is here presupposed, but still I think it worth while to call attention to certain important.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II
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Paperback. Condition: New. Print on Demand. This book delves into the intricate world of numbers, exploring their nature, meaning, and the profound concept of continuity. The author embarks on a captivating journey through the history of mathematical thought, tracing the evolution of number systems from the familiar realm of rational numbers to the enigmatic domain of irrational numbers. With meticulous precision, the author dissects the fundamental principles of arithmetic, unveiling the inherent limitations of rational numbers in capturing the essence of continuity. The concept of a "cut," a groundbreaking idea introduced by the author, bridges this gap, paving the way for the creation of irrational numbers and the establishment of a complete and continuous number system. This exploration extends beyond theoretical abstractions, delving into the practical implications of continuity in infinitesimal analysis. The author demonstrates the profound connection between the principles of continuity and fundamental theorems of calculus, illuminating the essential role of a continuous number domain in understanding the intricacies of change and motion. Ultimately, this book challenges our understanding of numbers as mere tools of calculation, revealing them as profound constructs that shape our comprehension of the world around us. The author's insights into the nature of continuity and the creation of irrational numbers revolutionized the field of mathematics, laying the groundwork for modern analysis and our understanding of the universe's underlying mathematical structure. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332011407_0
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Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II. the Nature and Meaning of Numbers (Classic Reprint)
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