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This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.
Content Level »Research
Keywords »Arithmetic - Equivalence - Finite - Mathematics - Set Theory - axiom of choice - cardinals - function - ksa - ordinal - well-ordering principle
I Exercises.- 1 First Axioms of the Theory NBG.- 2 Relations.- 3 Functional Relations and Mappings.- 4 Families of Sets.- 5 Equivalence Relations.- 6 Order Relations.- 7 Well-Ordering.- 8 Ordinals.- 9 Natural Numbers.- 10 Equivalents of the Axiom of Choice.- 11 Infinite Sets.- 12 Cardinals.- 13 Cardinal and Ordinal Arithmetic.- II Answers.- 14 Answers to Chapter 1.- 15 Answers to Chapter 2.- 16 Answers to Chapter 3.- 17 Answers to Chapter 4.- 18 Answers to Chapter 5.- 19 Answers to Chapter 6.- 20 Answers to Chapter 7.- 21 Answers to Chapter 8.- 22 Answers to Chapter 9.- 23 Answers to Chapter 10.- 24 Answers to Chapter 11.- 25 Answers to Chapter 12.- 26 Answers to Chapter 13.