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＜E-Book＞
Elements of Logic via Numbers and Sets / by D.L. Johnson
(Springer Undergraduate Mathematics Series. ISSN:21974144)

Edition	1st ed. 1998.
Publisher	London : Springer London : Imprint: Springer
Year	1998
Size	X, 188 p : online resource
Authors	*Johnson, D.L author SpringerLink (Online service)
Subjects	LCSH:Mathematical logic LCSH:Mathematics LCSH:Number theory FREE:Mathematical Logic and Foundations FREE:Mathematics FREE:Number Theory
Notes	1. Numbers -- 1.1 Arithmetic Progressions -- 1.2 Proof by Contradiction -- 1.3 Proof by Contraposition -- 1.4 Proof by Induction -- 1.5 Inductive Definition -- 1.6 The Well-ordering Principle -- 2. Logic -- 2.1 Propositions -- 2.2 Truth Tables -- 2.3 Syllogisms -- 2.4 Quantifiers -- 3. Sets -- 3.1 Introduction -- 3.2 Operations -- 3.3 Laws -- 3.4 The Power Set -- 4. Relations -- 4.1 Equivalence Relations -- 4.2 Congruences -- 4.3 Number Systems -- 4.4 Orderings -- 5. Maps -- 5.1 Terminology and Notation -- 5.2 Examples -- 5.3 Injections, Surjections and Bijections -- 5.4 Peano’s Axioms -- 6. Cardinal Numbers -- 6.1 Cardinal Arithmetic -- 6.2 The Cantor-Schroeder-Bernstein theorem -- 6.3 Countable Sets -- 6.4 Uncountable Sets -- Solutions to Exercises -- Guide to the Literature -- Dramatis Personae 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 HTTP:URL=https://doi.org/10.1007/978-1-4471-0603-6

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