Set theory : a first course
- New York : Cambridge University Press, 2016
- xii, 250 p. ; ill., 24 cm.
- Cambridge mathematical textbooks .
Includes bibliographical references and indexes.
Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
9781107120327
Cardinal numbers Ordinal numbers Axiom of choice Transfinite recursion; Abstract sets Axiomatic set theory