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Author: H. M. Hubey
Publisher: World Scientific
Published: 1998
Total Pages: 550
ISBN-13: 9789810230814
DOWNLOAD EBOOKCD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.
Author: Source Wikipedia
Publisher: University-Press.org
Published: 2013-09
Total Pages: 58
ISBN-13: 9781230630700
DOWNLOAD EBOOKPlease 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.
Author: Pravin Johri
Publisher: Createspace Independent Publishing Platform
Published: 2018-06-10
Total Pages: 98
ISBN-13: 9781720899778
DOWNLOAD EBOOKThe 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!
Author: Ian Stewart
Publisher: Oxford University Press
Published: 2017
Total Pages: 161
ISBN-13: 0198755236
DOWNLOAD EBOOKIan 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.
Author: Anthony C. Patton
Publisher: Algora Publishing
Published: 2018-07-01
Total Pages: 200
ISBN-13: 1628943416
DOWNLOAD EBOOKAuthor: John Stillwell
Publisher: CRC Press
Published: 2010-07-13
Total Pages: 202
ISBN-13: 1439865507
DOWNLOAD EBOOKWinner 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
Author: Anthony Gardiner
Publisher: Courier Corporation
Published: 2002-01-01
Total Pages: 324
ISBN-13: 9780486425382
DOWNLOAD EBOOKConceived 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.
Author: Shaughan Lavine
Publisher: Harvard University Press
Published: 2009-06-30
Total Pages: 262
ISBN-13: 0674265335
DOWNLOAD EBOOKAn 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
Author: Eugenia Cheng
Publisher: Profile Books
Published: 2017-03-09
Total Pages: 191
ISBN-13: 1782830812
DOWNLOAD EBOOKSHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Author: P.N. Shivakumar
Publisher: Springer
Published: 2016-06-20
Total Pages: 124
ISBN-13: 3319301802
DOWNLOAD EBOOKThis 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.
