Classic Set Theory: For Guided Independent Study
CRC Press, 1996. gada 1. jūl. - 296 lappuses
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:
The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.
Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
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Intro to ZF with more descriptive comments and worked examples than usual. Derived from Open Univeristy course. Lasīt pilnu pārskatu
The Real Numbers
The Natural Numbers
The ZermeloFraenkel Axioms
The Axiom of Choice
Cardinals without the Axiom of Choice
Set Theory with the Axiom of Choice
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addition argument arithmetic assuming axiom axiom of choice bijection called Cantor's cardinal chapter consisting construction contains contradiction corresponding countable course Dedekind define definition describe domain element equal equivalence example Exercise exists explain exploit fact finite fixed formal formula function f further give given idea important induction infinite sets initial instance involving language later least least element lemma less limit ordinal linear linearly ordered look mathematics means multiplication namely natural numbers non-empty notation Note objects one-one function operations order-isomorphic ordered pairs ordered sets partial order principle problem proof prove rationals real numbers recursion relation represent result result holds satisfies sequence set theory Solution sort statement subset successor Suppose Theorem transfinite true union unique upper bound usual well-ordered sets write