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Excerpt from Contributions to the Founding of the Theory of Transfinite Numbers
Hankel attempted to exhibit the theory of functions of a real variable as leading, of necessity, to the restrictions and extensions from which we start in Riemann's theory of functions of a complex variable and yet Hankel's researches entitle him to be called the founder of the independent theory of functions of a real variable. At about the same time, Heine initiated, under the direct influence of Riemann's Habilitationsschrift, a new series of investigations on trigonometrical series.
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Contributions to the Founding of the Theory of Transfinite Numbers
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Paperback. Condition: New. Print on Demand. This book delves into the fascinating evolution of mathematical thought during the 19th century, tracing the emergence and development of the theory of functions. The narrative unfolds against the backdrop of groundbreaking contributions from renowned mathematicians like Fourier, Cauchy, Riemann, and Weierstrass, each of whom played a pivotal role in shaping this field. Central to the book's exploration is the profound impact of these mathematicians' work on the understanding of mathematical concepts such as continuity, convergence, and the nature of numbers themselves. It meticulously examines the shift from a geometric understanding of numbers to a more rigorous, arithmetical foundation, highlighting the critical role of Weierstrass's theory of irrational numbers. Furthermore, the book delves into the pioneering work of Georg Cantor, who built upon these foundations to develop his groundbreaking theory of transfinite numbers. This theory extended the concept of numbers beyond the finite realm, revolutionizing the way mathematicians conceptualize infinity and its various orders. By illuminating the historical context and intellectual currents that shaped the theory of functions and transfinite numbers, this book provides invaluable insights into the intricate world of mathematical thought and its far-reaching implications for our understanding of the infinite. 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 # 9781330493045_0
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Contributions to the Founding of the Theory of Transfinite Numbers (Classic Reprint)
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330493045
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Contributions to the Founding of the Theory of Transfinite Numbers (Classic Reprint)
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330493045
Quantity: 15 available