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The Diagonal Infinity
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Book Synopsis The Diagonal Infinity by : H. M. Hubey
Download or read book The Diagonal Infinity written by H. M. Hubey and published by World Scientific. This book was released on 1998 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.
Download or read book Infinity written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 57. Chapters: Countable set, Cantor's diagonal argument, Surreal number, Continuum hypothesis, Hyperreal number, Extended real number line, Uncountable set, Where Mathematics Comes From, Absolute Infinite, Ultrafinitism, Infinitesimal, Infinite monkey theorem, Actual infinity, Non-standard calculus, Real projective line, Temporal finitism, Cardinality of the continuum, Aleph number, Beth number, Line at infinity, Plane at infinity, Apeirogon, Levi-Civita field, Point at infinity, Hyperplane at infinity, Infinity plus one, Superreal number, Hyperinteger, Circular points at infinity, Directed infinity, Amorphous set.
Book Synopsis Why the Cantor Diagonal Argument Is Not Valid by : Pravin Johri
Download or read book Why the Cantor Diagonal Argument Is Not Valid written by Pravin Johri and published by Createspace Independent Publishing Platform. This book was released on 2018-06-10 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cantor Diagonal Argument (CDA) is the quintessential result in Cantor's infinite set theory. This is one procedure that almost everyone who studies this subject finds astounding. However, mathematicians maintain that the CDA is absolutely correct and that the "countless" people trying to repudiate the CDA are not only wrong but are seemingly "irrational" enough to challenge such a widely accepted result.This book outlines all the different issues with the CDA. And, there are many.This book does not attempt to disprove the CDA by finding fault with it. Since the mathematical community has not bought into any of the tens of counterarguments it likely will ignore yet one more.Instead, assuming the CDA is correct, we create a situation where the CDA produces results when it really shouldn't and use the CDA itself to discredit the CDA.Cantor's infinite set theory is largely based on arbitrary rules, confounding axioms, and logic that defies intuition and common sense. Our previous books explain exactly what is wrong and why. The theory is hopelessly flawed because the starting assumption - the axiom of infinity - is wrong. There is no such thing as an infinite set. But mathematicians stubbornly stick to their belief that everything is correct.Hopefully this is the straw that breaks the camel's back!
Download or read book Infinity written by Ian Stewart and published by Oxford University Press. This book was released on 2017 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ian Stewart considers the concept of infinity and the profound role it plays in mathematics, logic, physics, cosmology, and philosophy. He shows that working with infinity is not just an abstract, intellectual exercise, and analyses its important practical everyday applications.
Book Synopsis The End of Infinity by : Anthony C. Patton
Download or read book The End of Infinity written by Anthony C. Patton and published by Algora Publishing. This book was released on 2018-07-01 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Roads to Infinity by : John Stillwell
Download or read book Roads to Infinity written by John Stillwell and published by CRC Press. This book was released on 2010-07-13 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h
Book Synopsis Understanding Infinity by : Anthony Gardiner
Download or read book Understanding Infinity written by Anthony Gardiner and published by Courier Corporation. This book was released on 2002-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.
Book Synopsis Understanding the Infinite by : Shaughan Lavine
Download or read book Understanding the Infinite written by Shaughan Lavine and published by Harvard University Press. This book was released on 2009-06-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
Book Synopsis Infinite Matrices and Their Recent Applications by : P.N. Shivakumar
Download or read book Infinite Matrices and Their Recent Applications written by P.N. Shivakumar and published by Springer. This book was released on 2016-06-20 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian.
Book Synopsis Classical Lie Algebras at Infinity by : Ivan Penkov
Download or read book Classical Lie Algebras at Infinity written by Ivan Penkov and published by Springer Nature. This book was released on 2022-01-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Book Synopsis Infinite Matrices and their Finite Sections by : Marko Lindner
Download or read book Infinite Matrices and their Finite Sections written by Marko Lindner and published by Springer Science & Business Media. This book was released on 2006-11-10 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.
Book Synopsis Zero to Infinity by : Peter Rowlands
Download or read book Zero to Infinity written by Peter Rowlands and published by World Scientific. This book was released on 2007 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rowlands offers researchers in quantum, theoretical and high energy physics immediate access to simple but powerful techniques.
Book Synopsis Infinity and the Mind by : Rudy Rucker
Download or read book Infinity and the Mind written by Rudy Rucker and published by Princeton University Press. This book was released on 2019-07-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.
Book Synopsis The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics by : James Haglund
Download or read book The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics written by James Haglund and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
Book Synopsis Higher Structures in Geometry and Physics by : Alberto S. Cattaneo
Download or read book Higher Structures in Geometry and Physics written by Alberto S. Cattaneo and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Book Synopsis The Future of Creation Order by : Gerrit Glas
Download or read book The Future of Creation Order written by Gerrit Glas and published by Springer. This book was released on 2018-01-12 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work provides an overview of attempts to assess the current condition of the concept of creation order within reformational philosophy compared to other perspectives. Focusing on the natural and life sciences, and theology, this first volume of two examines the arguments for and against the beauty, coherence and order shown in the natural world being related to the will or nature of a Creator. It examines the decay of a Deist universe, and the idea of the pre-givenness of norms, laws and structures as challenged by evolutionary theory and social philosophy. It describes the different responses to the collapse of order: that given by Christian philosophy scholars who still argue for the idea of a pre-given world order, and that of other scholars who see this idea of stable creation order and/or natural law as redundant and in need of a thorough rethinking. It studies the particular role that reformational philosophy has played in the discussion. It shows how, ever since its inception, almost a century ago, the concepts of order and law (principle, structure) have been at the heart of this philosophy, and that one way to characterise this tradition is as a philosophy of creation order. Reformational philosophers have maintained the notion of law as ‘holding’ for reality. This book discusses the questions that have arisen about the nature of such law: is it a religious or philosophical concept; does law just mean ‘orderliness’? How does it relate to laws of nature? Have they always existed or do they ‘emerge’ during the process of evolution?
Download or read book Naming Infinity written by Loren Graham and published by Harvard University Press. This book was released on 2009-03-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
