Elements of Logic via Numbers and Sets

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Springer Science & Business Media, 25 sept. 1998 - 188 pages
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
 

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Table des matières

Numbers
1
12 Proof by Contradiction
5
13 Proof by Contraposition
8
14 Proof by Induction
10
15 Inductive Definition
19
16 The Wellordering Principle
27
Logic
35
22 Truth Tables
39
43 Number Systems
79
44 Orderings
85
Maps
89
52 Examples
94
53 Injections Surjections and Bijections
99
54 Peanos Axioms
105
Cardinal Numbers
113
61 Cardinal Arithmetic
114

23 Syllogisms
43
24 Quantifiers
48
Sets
53
31 Introduction
54
32 Operations
58
33 Laws
62
34 The Power Set
65
Relations
71
41 Equivalence Relations
72
42 Congruences
75
62 The CantorSchroederBernstein theorem
118
63 Countable Sets
121
64 Uncountable Sets
126
Solutions to Exercises
131
Guide to the Literature
163
Bibliography
165
Dramatis Personae in approximate order of appearance
167
Index
171
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