Foundations of Analysis

Foundations of Analysis

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Description

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"" - also available from the AMS - answers these important questions.
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Product details

  • Hardback | 136 pages
  • 161.04 x 235.97 x 13.97mm | 317.51g
  • Providence, United States
  • English
  • Revised
  • 3rd Revised edition
  • 082182693X
  • 9780821826935
  • 458,245

Table of contents

Natural Numbers:; 1.1 Axioms; 1.2 Addition; 1.3 Ordering; 1.4 Multiplication Fractions:; 2.1 Definition and equivalence; 2.2 Ordering; 2.3 Addition; 2.4 Multiplication; 2.5 Rational numbers and integers Cuts:; 3.1 Definition; 3.2 Ordering; 3.3 Addition; 3.4 Multiplication; 3.5 Rational cuts and integral cuts Real Numbers:; 4.1 Definition; 4.2 Ordering; 4.3 Addition; 4.4 Multiplication; 4.5 Dedekind's fundamental theorem Complex Numbers:; 5.1 Definition; 5.2 Addition; 5.3 Multiplication; 5.4 Subtraction; 5.5 Division; 5.6 Complex conjugates; 5.7 Absolute value; 5.8 Sums and products; 5.9 Powers; 5.10 Incorporation of the real numbers into the system of complex numbers.
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Rating details

20 ratings
4.5 out of 5 stars
5 65% (13)
4 25% (5)
3 5% (1)
2 5% (1)
1 0% (0)
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