The Nature Of Infinitesimals
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The Nature Of Infinitesimals
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Author : Peter F. Erickson
language : en
Publisher: Xlibris Corporation
Release Date : 2006-05-05
The Nature Of Infinitesimals written by Peter F. Erickson and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-05 with Mathematics categories.
Erickson explores and explains the infinite and the infinitesimal with application to absolute space, time and motion, as well as absolute zero temperature in this thoughtful treatise. Mathematicians, scientists and philosophers have explored the realms of the continuous and discrete for centuries. Erickson delves into the history of these concepts and how people learn and understand them. He regards the infinitesimal as the key to understanding much of the scientific basis of the universe, and intertwines mathematical examples and historical context from Aristotle, Kant, Euler, Newton and more with his deductions-resulting in a readable treatment of complex topics. The reader will gain an understanding of potential versus actual infinity, irrational and imaginary numbers, the infinitesimal, and the tangent, among other concepts. At the heart of Ericksons work is the veritable number system, in which positive and negative numbers are incompatible for the basic mathematical operations of addition, subtraction, multiplication, division, roots and ratios. This number system, he demonstrates, can provide a new interpretation of imaginary numbers, as a combination of the real and the veritable. Erickson further explores limits, derivatives and integrals before turning his attention to non-Euclidean geometry. In each topic, he applies his new understanding of the infinitesimal to the ideas of mathematics and draws conclusions. In the case of non-Euclidean geometry, the author determines that its inconsistent with the infinitesimal. Erickson supplies illustrative examples both in words and images-he clearly defines new notation as needed for concepts such as eternity, the infinitesimal, the instant and an unlimited quantity. In the final chapters, the author addresses absolute space, time and motion through the lens of the infinitesimal. While explaining his deductions and thoughts on these complex topics, he raises new questions for his readers to contemplate, such as the origin of memory. A weighty tome for devotees of mathematics and physics that raises interesting questions.
Infinitesimal Differences
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Author : Ursula Goldenbaum
language : en
Publisher: Walter de Gruyter
Release Date : 2008-11-03
Infinitesimal Differences written by Ursula Goldenbaum and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-03 with Philosophy categories.
The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes.
An Elementary Course Of Infinitesimal Calculus
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Author : Sir Horace Lamb
language : en
Publisher:
Release Date : 1924
An Elementary Course Of Infinitesimal Calculus written by Sir Horace Lamb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1924 with Calculus categories.
A Primer Of Infinitesimal Analysis
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Author : John Lane Bell
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-28
A Primer Of Infinitesimal Analysis written by John Lane Bell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-28 with Mathematics categories.
This is the first elementary book to employ the concept of infinitesimals.
The Metaphysical Principles Of The Infinitesimal Calculus
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Author : René Guénon
language : en
Publisher: Sophia Perennis
Release Date : 2003
The Metaphysical Principles Of The Infinitesimal Calculus written by René Guénon and has been published by Sophia Perennis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
René Guénon (1886-1951) is undoubtedly one of the luminaries of the twentieth century, whose critique of the modern world has stood fast against the shifting sands of recent philosophies. His oeuvre of 26 volumes is providential for the modern seeker: pointing ceaselessly to the perennial wisdom found in past cultures ranging from the Shamanistic to the Indian and Chinese, the Hellenic and Judaic, the Christian and Islamic, and including also Alchemy, Hermeticism, and other esoteric currents, at the same time it directs the reader to the deepest level of religious praxis, emphasizing the need for affiliation with a revealed tradition even while acknowledging the final identity of all spiritual paths as they approach the summit of spiritual realization. Guénon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet threat throughout his doctrinal studies. In this late text published just five years before his death, Guénon devotes an entire volume to questions regarding the nature of limits and the infinite, both with respect to the calculus as a mathematical discipline, and to the symbolism of the initiatic path. This book therefore extends and complements the geometrical symbolism Guénon employs in several of his other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. A sampling of chapter titles will convey some sense of this remarkable work: 'Infinite and Indefinite', 'Degrees of Infinity', 'Zero is not a Number', 'The Law of Continuity', 'Vanishing Quantities', 'Various Orders of Indefinitude', 'The Arguments of Zeno of Elea', 'The True Conception of Passage to the Limit'. The Collected Works of René Guénon brings together the writings of one of the greatest prophets of our time, whose voice is even more important today than when he was alive. Huston Smith, author of The World's Religions, etc.
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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Author : John L. Bell
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics written by John L. Bell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Absolute Space Absolute Time And Absolute Motion
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Author : Peter F. Erickson
language : en
Publisher: Xlibris Corporation
Release Date : 2006
Absolute Space Absolute Time And Absolute Motion written by Peter F. Erickson and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Absolute Space, Absolute Time, and Absolute Motion exist. These are shown to be facts through an investigation of the nature of infinitesimals. Knowledge of that nature also makes the irrational magnitudes within the unit comprehensible. The number line is shown to be cognitively superior to set theory; furthermore, non-Euclidean geometry is shown to be a mere manipulation of symbols and not an expression of a "parallel universe." Inside, the reader will also learn about a hitherto unknown number system locked within _-1. He will also discover in the infinitesimal calculus a hidden key to a level of reality beneath that of nano-technology.. The foundation of science is not some vague generality, but the exercise of reason as originating from the human sensorium. There is no difference between mathematical and ordinary inductive reasoning.
Infinitesimal
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Author : Amir Alexander
language : en
Publisher: Simon and Schuster
Release Date : 2014-07-03
Infinitesimal written by Amir Alexander and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Science categories.
On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.
Stochastic Calculus With Infinitesimals
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Author : Frederik S. Herzberg
language : en
Publisher: Springer
Release Date : 2012-11-06
Stochastic Calculus With Infinitesimals written by Frederik S. Herzberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
The Elements Of The True Arithmetic Of Infinites
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Author : Thomas Taylor
language : en
Publisher:
Release Date : 1809
The Elements Of The True Arithmetic Of Infinites written by Thomas Taylor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1809 with Calculus categories.