Elements of Logic via Numbers and Sets

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Sprache: Englisch

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Beschreibung

This is an elementary text, aimed at first-year undergraduates, which has
been designed to bridge the gap between school and university mathematics
and to emphasise the importance of proofs - both how to follow a proof and
how to construct a proof. The book lays the foundation for most of the key
subjects studied in an undergraduate degree program, and provides numerous
exercises and a bibliography with suggestions for further and background
reading.

Zusammenfassung

Inhaltsverzeichnis

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.

Erscheinungsjahr:	1998
Fachbereich:	Grundlagen
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	x 188 S.
ISBN-13:	9783540761235
ISBN-10:	3540761233
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Johnson, D. L.
Hersteller:	Springer Springer Vieweg Springer-Verlag GmbH Springer Undergraduate Mathematics Series
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 178 x 11 mm
Von/Mit:	D. L. Johnson
Erscheinungsdatum:	14.01.1998
Gewicht:	0,338 kg