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The Number-System of Algebra (Classic Reprint): Treated Theoretically and Historically: Treated Theoretically and Historically (Classic Reprint) - Tapa blanda
Sinopsis
Discover how algebra’s symbols, roots, and imaginary ideas evolved—from Descartes to quaternions—and why they still shape math today.
This book surveys the number-system of algebra in a historical and theoretical light. It traces how symbolic notation, negative and imaginary numbers, and the idea of a continuous variable expanded the reach of mathematics. Through short, clear explanations, it connects old methods to modern ideas, showing how foundational concepts emerged and why they matter now.
- Learn how early notations and binomial thinking laid the groundwork for modern algebraic symbolism
- See how the negative and the imaginary were accepted as useful tools in advancing theory
- Explore the shift from geometry to the algebra of line segments and the rise of the continuous variable
- Understand how key figures like Descartes, Newton, Euler, and Hamilton shaped the number-system you use today
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Reseña del editor
Excerpt from The Number-System of Algebra: Treated Theoretically and Historically
Descartes' geometric algebra The continuous variable. Newton. Euler The general irrational.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
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.
Reseña del editor
Excerpt from The Number-System of Algebra: Treated Theoretically and Historically
The theoretical part of this little book is an elementary exposition of the nature of the number concept, of the positive integer, and of the four artificial forms of number which, with the positive integer, constitute the "number-system" of algebra, viz. the negative, the fraction, the irrational, and the imaginary. The discussion of the artificial numbers follows, in general, the same lines as my pamphlet: On the Forms of Number arising in Common Algebra, but it is much more exhaustive and thoroughgoing. The point of view is the one first suggested by Peacock and Gregory, and accepted by mathematicians generally since the discovery of quaternions and the Ausdehnungslehre of Grassmann, that algebra is completely defined formally by the laws of combination to which its fundamental operations are subject; that, speaking generally, these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This doctrine was fully developed for the negative, the fraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, and made complete by Cantor's beautiful theory of the irrational in 1871, but it has not as yet received adequate treatment in English.
Any large degree of originality in work of this kind is naturally out of the question.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
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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The Number-System of Algebra: Treated Theoretically and Historically
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Paperback. Condición: New. Print on Demand. This book offers a theoretical exploration of the nature of numbers, examining the positive integer and the four artificial forms of number â" the negative, fraction, irrational, and imaginary â" that, along with the positive integer, constitute the number system of algebra. The author provides an elementary exposition of these concepts, following in the footsteps of Peacock, Gregory, Hankel, Weierstrass, Cantor, and Thomae. The discussion of the artificial numbers largely adheres to the lines of the authorâs earlier work, On the Forms of Number arising in Common Algebra, but is more exhaustive and thorough. The author contends that algebra is completely defined formally by the laws of combination to which its fundamental operations are subject, and that these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This position was developed for the negative, fraction, and imaginary by Hankel in 1867, and made complete by Cantorâs beautiful theory of the irrational in 1871, but has yet to receive adequate treatment in English. 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. Nº de ref. del artículo: 9781330109908_0
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The Number-System of Algebra: Treated Theoretically and Historically (Classic Reprint)
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