Foundations of Analysis
著者
書誌事項
Foundations of Analysis
（AMS chelsea publishing）
American Mathematical Society ,c1966
3rd ed
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注記
Includes indexes
内容説明・目次
内容説明
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.
目次
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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