Foundations of Analysis
3rd Edition
Published on 30. January 1966
Book
Paperback/Softback
136 pages
978-1-4704-7057-9 (ISBN)
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 answers these important questions.
Reviews / Votes
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 MonthlyMore details
Series
Edition
Third Edition
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
College/higher education
Edition type
New edition
ISBN-13
978-1-4704-7057-9 (9781470470579)
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Schweitzer Classification
Content
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
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