Abstract
Publisher Summary An axiom system is formed by selecting its basic concepts and explaining the nature of those concepts. Then, the axioms for the concepts are written and proved to be true by explanation. This chapter presents the axioms of set theory in the same fashion and explains the notion of a set. The chapter also presents the development of set theory. The explanations given in the chapter are useful in justifying the axioms of set theory, for investigating new axioms, and proving theorems about sets. The chapter also discusses extensionality axiom, separation axiom, power set axiom, replacement axiom, infinity axiom, and regularity axiom,
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