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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... proof of Theorem 41. 11. Find an identity which will serve as a definition of intersection in terms of difference. 12. We define the operation of symmetric difference by the identity: 1. 2. 3. 4. A ÷ B = (A ~ B) ∪ (B ~A).
... symmetric difference and intersection. § 2.4 Pairing Axiom and Ordered Pairs. The three axioms considered so far permit us to prove the existence of only one set – the empty set. We now introduce the axiom which asserts that given any ...
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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 | |