ISBN-10:
3540761233
ISBN-13:
9783540761235
Pub. Date:
02/28/2001
Publisher:
Springer London
Elements of Logic via Numbers and Sets / Edition 1

Elements of Logic via Numbers and Sets / Edition 1

by D.L. Johnson

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Product Details

ISBN-13: 9783540761235
Publisher: Springer London
Publication date: 02/28/2001
Series: Springer Undergraduate Mathematics Series
Edition description: 1st ed. 1998. Corr. 2nd printing 1998
Pages: 188
Sales rank: 380,494
Product dimensions: 7.01(w) x 9.25(h) x 0.36(d)

Table of Contents

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.

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