Home » The Number System of Algebra: Number Systems from the Egyptians to the Greeks to the Europeans to Arabic by Henry Fine
The Number System of Algebra: Number Systems from the Egyptians to the Greeks to the Europeans to Arabic Henry Fine

The Number System of Algebra: Number Systems from the Egyptians to the Greeks to the Europeans to Arabic

Henry Fine

Published June 21st 2013
ISBN :
Kindle Edition
98 pages
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 About the Book 

I THEORETICAL1 THE POSITIVE INTEGER,AND THE LAWS WHICH REGULATE THE ADDITION ANDMULTIPLICATION OF POSITIVE INTEGERSThe number conceptNumerical equalityNumeral symbolsThe numerical equationCountingAddition and its lawsMultiplication andMoreI THEORETICAL1 THE POSITIVE INTEGER,AND THE LAWS WHICH REGULATE THE ADDITION ANDMULTIPLICATION OF POSITIVE INTEGERSThe number conceptNumerical equalityNumeral symbolsThe numerical equationCountingAddition and its lawsMultiplication and its laws2 SUBTRACTION AND THE NEGATIVE INTEGERNumerical subtractionDeterminateness of numerical subtractionFormal rules of subtractionLimitations of numerical subtractionSymbolic equationsPrinciple of permanence. Symbolic subtractionZeroThe negativeRecapitulation of the argument of the chapter3 DIVISION AND THE FRACTIONNumerical divisionDeterminateness of numerical divisionFormal rules of divisionLimitations of numerical divisionSymbolic division. The fractionNegative fractionsGeneral test of the equality or inequality of fractionsIndeterminateness of division by zeroDeterminateness of symbolic divisionThe vanishing of a productThe system of rational numbers4 THE IRRATIONALInadequateness of the system of rational numbersNumbers defined by regular sequences. The irrationalGeneralized definitions of zero, positive, negativeOf the four fundamental operationsOf equality and greater and lesser inequalityThe number defined by a regular sequence its limiting valueDivision by zeroThe number-system defined by regular sequences of rationals a closed and continuous system5 THE IMAGINARY COMPLEX NUMBERSThe pure imaginaryComplex numbersThe fundamental operations on complex numbersNumerical comparison of complex numbersAdequateness of the system of complex numberFundamental characteristics of the algebra of number6 GRAPHICAL REPRESENTATION OF NUMBERS THE VARIABLE.Correspondence between the real number-system and the points of a lineThe continuous variableCorrespondence between the complex number-system and the points of a planeThe complex variableDefinitions of modulus and argument of a complex number and of sine,cosine, and circular measure of an angleConstruction of the points which represent the sum, difference, product,and quotient of two complex numbers7 THE FUNDAMENTAL THEOREM OF ALGEBRADefinitions of the algebraic equation and its rootsDemonstration that an algebraic equation of the nth degree has n roots8 INFINITE SERIES8.1 REAL SERIESDefinitions of sum, convergence, and divergenceGeneral test of convergenceAbsolute and conditional convergenceSpecial tests of convergenceLimits of convergenceThe fundamental operations on infinite series8.2 COMPLEX SERIESGeneral test of convergenceAbsolute and conditional convergenceThe region of convergenceA theorem respecting complex seriesThe fundamental operations on complex series9 THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS UNDETERMINED COEFFICIENTS. INVOLUTION AND EVOLUTION. THE BINOMIAL THEOREMDefinition of functionFunctional equation of the exponential functionUndetermined coefficientsThe exponential functionThe functions sine and cosinePeriodicity of these functionsThe logarithmic functionIndeterminateness of logarithms