AMS Chelsea Publishing 1966; 136 pp; hardcover Volume: 79 Reprint/Revision History: first AMS printing 2001 ISBN10: 082182693X ISBN13: 9780821826935 List Price: US$30 Member Price: US$27 Order Code: CHEL/79.H
 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 Analysisalso available from the AMSanswers these important questions. Reviews "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 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
