Synopsis
I THEORETICAL 1 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 SERIES 8.1 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 HISTORICAL 10 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 NEGATIVE 16 RECOGNITION OF THE PURELY SYMBOLIC CHARACTERS OF ALGEBRA
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Présentation de l'éditeur
I THEORETICAL 1 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 SERIES 8.1 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 HISTORICAL 10 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 NEGATIVE 16 RECOGNITION OF THE PURELY SYMBOLIC CHARACTERS OF ALGEBRA
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The Number System of Algebra
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CreateSpace Independent Publishing Platform, 2013
ISBN 10 : 1490505016
ISBN 13 : 9781490505015
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Vendeur : Revaluation Books, Exeter, Royaume-Uni
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Paperback. Etat : Brand New. 94 pages. 9.00x6.00x0.22 inches. This item is printed on demand. N° de réf. du vendeur zk1490505016
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