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51693144-Landau-E-Foundations-of-Analysis-1966.pdf
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To those who want to know about the construction of number and gain deep insight of mathematical analysis, you are advised to read this book.
Table of Contents
Natural Numbers:
1.1 Axioms;
1.2 Addition;
1.3 Ordering;
1.4 Multiplication Fractions;
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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