Author | Johnson, D. L. author |
---|---|
Title | Elements of Logic via Numbers and Sets [electronic resource] / by D. L. Johnson |
Imprint | London : Springer London : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0603-6 |
Descript | X, 188 p. online resource |
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 Peanoโs 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