Foundations of Analysis

AvEdmund Landau

Häftad, Engelska, 1966

Del i serien AMS Chelsea Publishing

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Beskrivning

Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, what are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege, and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis answers these important questions.

Produktinformation

Utgivningsdatum:1966-01-30
Format:Häftad
Språk:Engelska
Serie:AMS Chelsea Publishing
Antal sidor:136
Upplaga:3
Förlag:American Mathematical Society
ISBN:9781470470579

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

Certainly no clearer treatment of the foundations of the number system can be offered … one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius."" —American Mathematical Monthly

Innehållsförteckning

Natural Numbers: 1.1 Axioms1.2 Addition1.3 Ordering1.4 MultiplicationFractions: 2.1 Definition and equivalence2.2 Ordering2.3 Addition2.4 Multiplication2.5 Rational numbers and integersCuts: 3.1 Definition3.2 Ordering3.3 Addition3.4 Multiplication3.5 Rational cuts and integral cutsReal Numbers: 4.1 Definition4.2 Ordering4.3 Addition4.4 Multiplication4.5 Dedekind's fundamental theoremComplex Numbers: 5.1 Definition5.2 Addition5.3 Multiplication5.4 Subtraction5.5 Division5.6 Complex conjugates5.7 Absolute value5.8 Sums and products5.9 Powers5.10 Incorporation of the real numbers into the system of complex numbers