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Classic Set Theory
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 definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers
Defining natural numbers in terms of sets
The potential paradoxes in set theory
The Zermelo-Fraenkel axioms for set theory
The axiom of choice
The arithmetic of ordered sets
Cantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.
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.
The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers
Defining natural numbers in terms of sets
The potential paradoxes in set theory
The Zermelo-Fraenkel axioms for set theory
The axiom of choice
The arithmetic of ordered sets
Cantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.
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.
- GenresMathematics
287 pages, Paperback
First published July 1, 1996
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Displaying 1 - 2 of 2 reviews
August 5, 2020
This book is for everything except for independent study:
1) Many many proofs are left as exercise (sometimes even definitions!)
2) The exercises are mostly explanations and not real exercises (so we can say that there are no real exercises at all).
3) After a concept has been introduced an example is almost never given (just a very few times).
4) An errata of the book is nowhere to be found.
5) The order of the chapters is unusual.
6) There are no solutions for the exercises at the end of each chapter.
One of the worst textbooks I've ever used unfortunately for these reasons
1) Many many proofs are left as exercise (sometimes even definitions!)
2) The exercises are mostly explanations and not real exercises (so we can say that there are no real exercises at all).
3) After a concept has been introduced an example is almost never given (just a very few times).
4) An errata of the book is nowhere to be found.
5) The order of the chapters is unusual.
6) There are no solutions for the exercises at the end of each chapter.
One of the worst textbooks I've ever used unfortunately for these reasons
April 21, 2023
Отличный учебник. Идеально подходит для самостоятельного изучения аксиоматической теории множеств.
Displaying 1 - 2 of 2 reviews