The Number System Of Algebra
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The Number System Of Algebra
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Author : Henry Burchard Fine
language : en
Publisher:
Release Date : 1890
The Number System Of Algebra written by Henry Burchard Fine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1890 with Algebra categories.
The Number System
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Author : H. A. Thurston
language : en
Publisher: Courier Corporation
Release Date : 2012-10-23
The Number System written by H. A. Thurston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-23 with Mathematics categories.
This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
The Number Systems Foundations Of Algebra And Analysis
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Author : Solomon Feferman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Number Systems Foundations Of Algebra And Analysis written by Solomon Feferman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Number theory categories.
The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''
Real World Numbers
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Author : Matthew Hill
language : en
Publisher: AuthorHouse
Release Date : 2011-12
Real World Numbers written by Matthew Hill and has been published by AuthorHouse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12 with Education categories.
This book provides support in keeping with the major goals of National Council of Teachers of Mathematics curriculum. It provides an important mathematical topic, the number system, which will be learned through K-8th grade, and used through high school and college. The instructional emphasis is designed to communicate knowledge and skills in mathematics across different grade levels, while offering the opportunity for children to learn about the number system in a fun and easy way. The book focuses on key areas of important emphasis, necessary for building math fluency in pre-algebra and algebra.
The Number Systems Of Analysis
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Author : Charles Huw Crawford Little
language : en
Publisher: World Scientific
Release Date : 2003
The Number Systems Of Analysis written by Charles Huw Crawford Little and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
The Number System Of Algebra
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Author : Henry B Fine
language : en
Publisher:
Release Date : 2019-12-14
The Number System Of Algebra written by Henry B Fine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-14 with categories.
The theoretical part of this little book is an elementary exposition of the nature of the number concept, of the positive integer, and of the four artificial forms of number which, with the positive integer, constitute the \number-system" of algebra, viz. the negative, the fraction, the irrational, and the imaginary. The discussion of the artificial numbers follows, in general, the same lines as my pamphlet: On the Forms of Number arising in Common Algebra, but it is much more exhaustive and thorough-going. The point of view is the one first suggested by Peacock and Gregory, and accepted bymathematicians generally since the discovery of quaternions and the Ausdehnungslehre of Grassmann, that algebra is completely defined formally by the laws of combination to which its fundamental operations are subject; that, speaking generally, these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This doctrine was fully developed for the negative, the fraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, and made complete by Cantor's beautiful theory of the irrational in 1871, but it has notas yet received adequate treatment in English.
The Number System Of Algebra Treated Theoretically And Historically
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Author : Henry Burchard Fine
language : en
Publisher:
Release Date : 1900
The Number System Of Algebra Treated Theoretically And Historically written by Henry Burchard Fine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with Algebra categories.
The Number System Of Algebra
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Author : Henry Fine
language : en
Publisher:
Release Date : 2013-06-23
The Number System Of Algebra written by Henry Fine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-23 with categories.
I THEORETICAL1 THE POSITIVE INTEGER, AND THE LAWS WHICH REGULATE THE ADDITION AND MULTIPLICATION OF POSITIVE INTEGERS The number concept Numerical equality Numeral symbols The numerical equation Counting Addition and its laws Multiplication and its laws 2 SUBTRACTION AND THE NEGATIVE INTEGER Numerical subtraction Determinateness of numerical subtraction Formal rules of subtraction Limitations of numerical subtraction Symbolic equations Principle of permanence. Symbolic subtraction Zero The negative Recapitulation of the argument of the chapter 3 DIVISION AND THE FRACTION Numerical division Determinateness of numerical division Formal rules of division Limitations of numerical division Symbolic division. The fraction Negative fractions General test of the equality or inequality of fractions Indeterminateness of division by zero Determinateness of symbolic division The vanishing of a product The system of rational numbers 4 THE IRRATIONAL Inadequateness of the system of rational numbers Numbers defined by regular sequences. The irrational Generalized definitions of zero, positive, negative Of the four fundamental operations Of equality and greater and lesser inequality The number defined by a regular sequence its limiting value Division by zero The number-system defined by regular sequences of rationals a closed and continuous system 5 THE IMAGINARY COMPLEX NUMBERS The pure imaginary Complex numbers The fundamental operations on complex numbers Numerical comparison of complex numbers Adequateness of the system of complex number Fundamental characteristics of the algebra of number 6 GRAPHICAL REPRESENTATION OF NUMBERS THE VARIABLE. Correspondence between the real number-system and the points of a line The continuous variable Correspondence between the complex number-system and the points of a plane The complex variable Definitions of modulus and argument of a complex number and of sine, cosine, and circular measure of an angle Construction of the points which represent the sum, difference, product, and quotient of two complex numbers 7 THE FUNDAMENTAL THEOREM OF ALGEBRA Definitions of the algebraic equation and its roots Demonstration that an algebraic equation of the nth degree has n roots 8 INFINITE SERIES8.1 REAL SERIES Definitions of sum, convergence, and divergence General test of convergence Absolute and conditional convergence Special tests of convergence Limits of convergence The fundamental operations on infinite series 8.2 COMPLEX SERIES General test of convergence Absolute and conditional convergence The region of convergence A theorem respecting complex series The fundamental operations on complex series 9 THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS UNDETERMINED COEFFICIENTS. INVOLUTION AND EVOLUTION. THE BINOMIAL THEOREM Definition of function Functional equation of the exponential function Undetermined coefficients The exponential function The functions sine and cosine Periodicity of these functions The logarithmic function Indeterminateness of logarithms Permanence of the laws of exponents Permanence of the laws of logarithms Involution and evolution The binomial theorem for complex exponents II HISTORICAL10 PRIMITIVE NUMERALS Gesture symbols Spoken symbols Written symbols 11 HISTORIC SYSTEMS OF NOTATION Egyptian and Phoenician Greek Roman Indo-Arabic 12 THE FRACTION Primitive fractions Roman fractions Egyptian (the Book of Ahmes) Babylonian or sexagesimal Greek 13 ORIGIN OF THE IRRATIONAL Discovery of irrational lines. Pythagoras Consequences of this discovery in Greek mathematics Greek approximate values of irrationals 14 ORIGIN OF THE NEGATIVE AND THE IMAGINARY.15 ACCEPTANCE OF THE NEGATIVE16 RECOGNITION OF THE PURELY SYMBOLIC CHARACTERS OF ALGEBRA
The Number System Of Algebra
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Author : Henry B Fine
language : en
Publisher:
Release Date : 2019-12-02
The Number System Of Algebra written by Henry B Fine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with categories.
THENUMBER-SYSTEM OF ALGEBRATREATED THEORETICALLY AND HISTORICALLY
The Number System Of Algebra
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Author : Henry B. Fine
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-09-19
The Number System Of Algebra written by Henry B. Fine and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with categories.
IN this book, are treated concisely the following subjects: I. Theoretical. The Positive Integer; Subtraction and the Negative Integer; Division and the Fraction; The Irrational; The Imaginary and Complex Numbers: Graphical Representations of Numbers; The Fundamental Theorem of Algebra; Defined by infinite series; The Exponential and Logarithmic Functions. II. Historical. The Primitive Numerals; Historic System of Notation; The Fraction; Origin of the Irrationals; Origin of the Negative and the Imaginary; Acceptance of the Negative, the general Irrational, and the Imaginary as Numbers: Recognition of the Purely Symbolic Nature of Algebra. This little book should be read by every teacher of Algebra and by every student desiring to pursue the Modern Higher Mathematical Analysis. The theoretical part is very instructive and the historical part full of many interesting facts. --The American Mathematical Monthly, Vol. 1