Axiomatic Set TheoryCourier Corporation, 4 mai 2012 - 265 pages One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: "Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. |
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... numbers. The Schröder-Bernstein Theorem is proved early in the chapter. The development of the theory of finite sets follows closely Alfred Tarski's well known article ... real numbers is given in detail. Cauchy sequences of rational numbers.
Patrick Suppes. numbers is given in detail. Cauchy sequences of rational numbers rather than Dedekind cuts are used to define the real numbers. Most of the elementary facts about sets of the power of the continuum are proved in the final ...
... real numbers, is suitable for an undergraduate mathematics course in the foundations of analysis, or as auxiliary reading for the course in the theory of functions of a real variable. This book was begun in 1954 as a set of lecture ...
... REAL NUMBERS 6.1 Introduction 6.2 Fractions 6.3 Non-negative Rational Numbers 6.4 Rational Numbers 6.5 Cauchy Sequences of Rational Numbers 6.6 Real Numbers 6.7 Sets of the Power of the Continuum 7. TRANSFINITE INDUCTION AND ORDINAL ...
... integers, rational numbers and real numbers has been a central problem for the classical researches of Weierstrass, Dedekind, Kronecker, Frege, Peano, Russell, Whitehead, Brouwer, and others. Perplexities about the nature of number did ...
Table des matières
RELATIONS AND FUNCTIONS | |
EQUIPOLLENCE FINITE SETS AND CARDINAL NUMBERS | |
FINITE ORDINALS AND DENUMERABLE SETS | |
RATIONAL NUMBERS AND REAL NUMBERS | |
TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC | |
THE AXIOM OF CHOICE | |
REFERENCES | |
AUTHOR INDEX | |