The Logic Of Number

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Charles S. Peirce on the Logic of Number

Author : Paul Shields
Publisher :
ISBN 13 : 9780983700470
Total Pages : 134 pages
Book Rating : 4.7/5 (4 download)

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Book Synopsis Charles S. Peirce on the Logic of Number by : Paul Shields

Download or read book Charles S. Peirce on the Logic of Number written by Paul Shields and published by . This book was released on 2012-10-24 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1881 the American philosopher Charles S. Peirce published a remarkable paper in The American Journal of Mathematics called "On the Logic of Number." Peirce's paper marked a watershed in nineteenth century mathematics, providing the first successful axiom system for the natural numbers. Awareness that Peirce's axiom system exists has been gradually increasing but the conventional wisdom among mathematicians is still that the first satisfactory axiom systems were those of Dedekind and Peano. The book analyzes Peirce's paper in depth, placing it in the context of contemporary work, and provides a proof of the equivalence of the Peirce and Dedekind axioms for the natural numbers.

Elements of Logic via Numbers and Sets

Author : D.L. Johnson
Publisher : Springer Science & Business Media
ISBN 13 : 1447106032
Total Pages : 179 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Elements of Logic via Numbers and Sets by : D.L. Johnson

Download or read book Elements of Logic via Numbers and Sets written by D.L. Johnson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Mathematical Logic with Special Reference to the Natural Numbers

Author : S. W. P. Steen
Publisher : Cambridge University Press
ISBN 13 : 9780521090582
Total Pages : 0 pages
Book Rating : 4.0/5 (95 download)

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Book Synopsis Mathematical Logic with Special Reference to the Natural Numbers by : S. W. P. Steen

Download or read book Mathematical Logic with Special Reference to the Natural Numbers written by S. W. P. Steen and published by Cambridge University Press. This book was released on 2008-11-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body of the text is rigorous, but, a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography.

The Logic of Number

Author : Neil Tennant
Publisher : Oxford University Press
ISBN 13 : 0192846671
Total Pages : 376 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis The Logic of Number by : Neil Tennant

Download or read book The Logic of Number written by Neil Tennant and published by Oxford University Press. This book was released on 2022-02-25 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops Tennant's Natural Logicist account of the foundations of the natural, rational, and real numbers. Tennant uses this framework to distinguish the logical from the intuitive aspects of the basic elements of arithmetic.

The Logic of Infinity

Author : Barnaby Sheppard
Publisher : Cambridge University Press
ISBN 13 : 1107058317
Total Pages : 498 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis The Logic of Infinity by : Barnaby Sheppard

Download or read book The Logic of Infinity written by Barnaby Sheppard and published by Cambridge University Press. This book was released on 2014-07-24 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

Logic, Sets, and Numbers

Author : Frank Blume
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781973779360
Total Pages : 240 pages
Book Rating : 4.7/5 (793 download)

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Book Synopsis Logic, Sets, and Numbers by : Frank Blume

Download or read book Logic, Sets, and Numbers written by Frank Blume and published by Createspace Independent Publishing Platform. This book was released on 2017-07-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic, Sets, and Numbers is a brief introduction to abstract mathematics that is meant to familiarize the reader with the formal and conceptual rigor that higher-level undergraduate and graduate textbooks commonly employ. Beginning with formal logic and a fairly extensive discussion of concise formulations of mathematical statements, the text moves on to cover general patterns of proofs, elementary set theory, mathematical induction, cardinality, as well as, in the final chapter, the creation of the various number systems from the integers up to the complex numbers. On the whole, the book's intent is not only to reveal the nature of mathematical abstraction, but also its inherent beauty and purity.

Handbook of Research on Global Media’s Preternatural Influence on Global Technological Singularity, Culture, and Government

Author : Schafer, Stephen Brock
Publisher : IGI Global
ISBN 13 : 179988886X
Total Pages : 522 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Handbook of Research on Global Media’s Preternatural Influence on Global Technological Singularity, Culture, and Government by : Schafer, Stephen Brock

Download or read book Handbook of Research on Global Media’s Preternatural Influence on Global Technological Singularity, Culture, and Government written by Schafer, Stephen Brock and published by IGI Global. This book was released on 2022-02-11 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trends of the last few years, including global health crises, political division, and the ongoing threat to social-environmental survival, have been continually obscured by disinformation and misinformation and therefore created a need for stronger global technological media policy. It is no longer acceptable or moral to support a global communication network based only on market factors and propaganda. The Handbook of Research on Global Media’s Preternatural Influence on Global Technological Singularity, Culture, and Government views preternatural healing of the media-sphere from a variety of perspectives on the dynamic of heart-coherent entertainment. Specifically, it addresses the subject of a healthy media from a variety of fractal perspectives. Covering topics such as collective unconscious, mediated reality, and government media trust, this major reference work is an essential resource for librarians, media specialists, media analysts, sociologists, government employees, communications specialists, psychologists, researchers, educators, academicians, and students.

Mathematical Logic

Author : Roman Kossak
Publisher : Springer
ISBN 13 : 3319972987
Total Pages : 186 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Mathematical Logic by : Roman Kossak

Download or read book Mathematical Logic written by Roman Kossak and published by Springer. This book was released on 2018-10-03 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Hilbert’s Tenth Problem: An Introduction to Logic, Number Theory, and Computability

Author : M. Ram Murty
Publisher : American Mathematical Soc.
ISBN 13 : 1470443996
Total Pages : 256 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hilbert’s Tenth Problem: An Introduction to Logic, Number Theory, and Computability by : M. Ram Murty

Download or read book Hilbert’s Tenth Problem: An Introduction to Logic, Number Theory, and Computability written by M. Ram Murty and published by American Mathematical Soc.. This book was released on 2019-05-09 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists. This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.

The Times MindGames Number and Logic Puzzles Book 1: 500 Brain-Crunching Puzzles, Featuring 7 Popular Mind Games (the Times Puzzle Books)

Author : The Times Mind Games
Publisher : Times Books
ISBN 13 : 9780008190309
Total Pages : 0 pages
Book Rating : 4.1/5 (93 download)

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Book Synopsis The Times MindGames Number and Logic Puzzles Book 1: 500 Brain-Crunching Puzzles, Featuring 7 Popular Mind Games (the Times Puzzle Books) by : The Times Mind Games

Download or read book The Times MindGames Number and Logic Puzzles Book 1: 500 Brain-Crunching Puzzles, Featuring 7 Popular Mind Games (the Times Puzzle Books) written by The Times Mind Games and published by Times Books. This book was released on 2016-09-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Test your powers of logic and mental agility with this mixed collection of 500 number and logic puzzles from the MindGames section of the Times. Puzzles include the favorites Suko, Brain Trainer, Cell Blocks, Futoshiki, Kakuro, Set Square, and KenKen. The perfect gift for all number and logic puzzle enthusiasts.

Good Math

Author : Mark C. Chu-Carroll
Publisher : Pragmatic Bookshelf
ISBN 13 : 168050360X
Total Pages : 269 pages
Book Rating : 4.6/5 (85 download)

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Book Synopsis Good Math by : Mark C. Chu-Carroll

Download or read book Good Math written by Mark C. Chu-Carroll and published by Pragmatic Bookshelf. This book was released on 2013-07-18 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.

Introduction to Higher-Order Categorical Logic

Author : J. Lambek
Publisher : Cambridge University Press
ISBN 13 : 9780521356534
Total Pages : 308 pages
Book Rating : 4.3/5 (565 download)

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Book Synopsis Introduction to Higher-Order Categorical Logic by : J. Lambek

Download or read book Introduction to Higher-Order Categorical Logic written by J. Lambek and published by Cambridge University Press. This book was released on 1988-03-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

A First Course in Discrete Mathematics

Author : Brian Lian
Publisher : Springer Science & Business Media
ISBN 13 : 9781852332365
Total Pages : 212 pages
Book Rating : 4.3/5 (323 download)

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Book Synopsis A First Course in Discrete Mathematics by : Brian Lian

Download or read book A First Course in Discrete Mathematics written by Brian Lian and published by Springer Science & Business Media. This book was released on 2000-10-27 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.

The Logic of Quantum Mechanics: Volume 15

Author : Enrico G. Beltrametti
Publisher : Cambridge University Press
ISBN 13 : 9780521168496
Total Pages : 340 pages
Book Rating : 4.1/5 (684 download)

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Book Synopsis The Logic of Quantum Mechanics: Volume 15 by : Enrico G. Beltrametti

Download or read book The Logic of Quantum Mechanics: Volume 15 written by Enrico G. Beltrametti and published by Cambridge University Press. This book was released on 2010-12-09 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.

A Tour Through Mathematical Logic

Author : Robert S. Wolf
Publisher : American Mathematical Soc.
ISBN 13 : 161444028X
Total Pages : 397 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis A Tour Through Mathematical Logic by : Robert S. Wolf

Download or read book A Tour Through Mathematical Logic written by Robert S. Wolf and published by American Mathematical Soc.. This book was released on 2005-12-31 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.

Logic in Elementary Mathematics

Author : Robert M. Exner
Publisher : Courier Corporation
ISBN 13 : 0486482219
Total Pages : 290 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Logic in Elementary Mathematics by : Robert M. Exner

Download or read book Logic in Elementary Mathematics written by Robert M. Exner and published by Courier Corporation. This book was released on 2011-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Topics include axiomatic structure and the relation of theory to interpretation. No prior training in logic is necessary, and numerous examples and exercises aid in the mastery of the language of logic. 1959 edition"--

Numbers & Logic: Kindergarten Workbook (Little Genius Series)

Author : flipClass
Publisher : flipClass
ISBN 13 : 8193439260
Total Pages : 142 pages
Book Rating : 4.1/5 (934 download)

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Book Synopsis Numbers & Logic: Kindergarten Workbook (Little Genius Series) by : flipClass

Download or read book Numbers & Logic: Kindergarten Workbook (Little Genius Series) written by flipClass and published by flipClass. This book was released on 2019-02-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Little Genius by flipClass is a series of high quality, engaging workbooks for Pre-schoolers/ Kindergarten students. Little Genius books series for Kindergarten includes all the multiple topics/concepts a child learns at this age. The books are prepared by expert teachers and experienced academicians. The books are packed with plenty of learning activities to make learning fun and interactive. Numbers and Logic Workbook introduces your child to Numbers, Ordinal Numbers, Addition & Subtraction, Time Telling, Money, Data Interpretation, Shapes, Patterns, Mathematical Logic, Ascending & Descending Order. Your child will not only learn, but also be able to apply these concepts to the surroundings. Learning Outcomes 1. Child will be able to identify, read, write and count numbers. 2. Child will be able to relate numbers with his/her surroundings. Example: a car has 4 wheels, 6 donuts in a tray etc. 3. Child will be able to count, add & subtract with the help of his/her fingers. 4. Child will be able to identify various simple shapes - square, circle, rectangle, triangle. 5. Child will be able to relate these shapes with the various everyday objects - rectangular flag, circular plates etc. 6. Child will be able to compare the quantity, size, weight, length and other approximate physical attributes of various objects. Example: a football is larger than a golf ball, a bus is taller than a car, a pencil is longer than an crayon etc. All concepts in this book are explained with plenty of illustrations to keep your child interested and engaged. These activities also help reinforce this learning in your child. Happy Learning.