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Schaum's Outlines contain hundreds of solutions to problems covered in any college course. This guide, which can be used with any text or can stand alone, contains at the beginning of each chapter a list of key definitions, a summary of major concepts, step by step solutions to dozens of problems, and additional practice problems. Major topics covered are Part I: Elementary Theory of Sets: Sets and Subsets , Basic Set Operations , Sets of Numbers , Functions , Product Sets and Graphs of Functions , Relations , Further Theory of Sets , Further Theory of Functions , Operations , Part II: Ordinals, Cardinals, and Transfinite Induction: Cardinal Numbers , Partially and Totally Ordered Sets , Well-Ordered Sets , Ordinal Numbers , Axiom of Choice , Zorn's Lemma, Well-Ordering Theorem , Paradoxes in Set Theory , Part III: Related Topics: Algebra of Propositions , Quantifiers , Boolean Algebra , and Logical Reasoning
This will be a revision of the first edition published in 1964 and will introduce current topics such as Turning Machines and Computable Functions. Some outdated chapters on sets relating to new math will be removed. Problems will be improved in the Ordinals, Cardinals, and Transfinite Induction chapters.
Sets and Subsets.
Basic Set Operators.
Sets of Numbers.
Functions.
Product Sets and Graphs of Functions.
Relations.
Further Theory of Sets.
Further Theory of Functions, Operations.
Cardinal Numbers.
Partially and Totally Ordered Sets.
Well-Ordered Sets/Ordinal Numbers.
Axiom of Choice.
Paradoxes in Set Theory.
Algebra of Propositions.
Quantifiers.
Boolean Algebra.
Logical Reasoning
Schaum's Outlines contain hundreds of solutions to problems covered in any college course. This guide, which can be used with any text or can stand alone, contains at the beginning of each chapter a list of key definitions, a summary of major concepts, step by step solutions to dozens of problems, and additional practice problems. Major topics covered are Part I: Elementary Theory of Sets: Sets and Subsets , Basic Set Operations , Sets of Numbers , Functions , Product Sets and Graphs of Functions , Relations , Further Theory of Sets , Further Theory of Functions , Operations , Part II: Ordinals, Cardinals, and Transfinite Induction: Cardinal Numbers , Partially and Totally Ordered Sets , Well-Ordered Sets , Ordinal Numbers , Axiom of Choice , Zorn's Lemma, Well-Ordering Theorem , Paradoxes in Set Theory , Part III: Related Topics: Algebra of Propositions , Quantifiers , Boolean Algebra , and Logical Reasoning
This will be a revision of the first edition published in 1964 and will introduce current topics such as Turning Machines and Computable Functions. Some outdated chapters on sets relating to new math will be removed. Problems will be improved in the Ordinals, Cardinals, and Transfinite Induction chapters.
Table of Contents
Sets and Subsets.
Basic Set Operators.
Sets of Numbers.
Functions.
Product Sets and Graphs of Functions.
Relations.
Further Theory of Sets.
Further Theory of Functions, Operations.
Cardinal Numbers.
Partially and Totally Ordered Sets.
Well-Ordered Sets/Ordinal Numbers.
Axiom of Choice.
Paradoxes in Set Theory.
Algebra of Propositions.
Quantifiers.
Boolean Algebra.
Logical Reasoning