Introduction to set theory
Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
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Relations Functions and Orderings
7 other sections not shown
algebraic Axiom of Choice Axiom of Constructibility Axiom of Determinacy Axiom Schema axiomatic binary operation binary relation called Chapter choice function computation of length conclude constructible model Continuum Hypothesis contradiction Corollary countable set Dedekind defined Definition Let denote domain endpoints equipotent equivalence example Exercises 1.1 exists finite sequence finite sets greatest element Hamel basis Hint holds implies inaccessible cardinals Induction Principle infimum infinite sets initial ordinal intuitively isomorphism least element least ordinal limit ordinal linearly ordered set mathematical maximal element n-tuples natural numbers nonempty subset notation one-to-one function one-to-one mapping ordered pairs ordinal number pairwise disjoint partition positive integers Proof prove rational numbers reader real numbers set of real set-theoretic Similarly supremum system of sets Theorem Let tion transfinite induction Transfinite Recursion transitive union unique upper bound verify well-orderable well-ordered set