Verfügbarkeit: 100 % mathematical proof | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Garnier, Rowan (VerfasserIn), Taylor, John 1957- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Chichester [u.a.] Wiley 1996
Schlagwörter:	Bewijstheorie Logic, Symbolic and mathematical Proof theory Beweistheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007360178&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	VIII, 317 S. Ill., graph. Darst.
ISBN:	047196199X

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Datensatz im Suchindex

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adam_text	100% MATHEMATICAL PROOF ROWAN GAMIER RICHMOND COLLEGE, LONDON JOHN TAYLOR UNIVERSITY OF BRIGHTON, SUSSEX JOHN WILEY & SONS CHICHESTER * NEW YORK * BRISBANE * TORONTO * SINGAPORE CONTENTS PREFACE VII 1 PROOFS, MATHEMATICAL AND NON-MATHEMATICAL 1 1.1 INTRODUCTION 1 1.2 INDUCTIVE AND DEDUCTIVE REASONING 2 1.3 A PROOF OR NOT A PROOF? 5 2 PROPOSITIONAL LOGIC 15 2.1 PROPOSITIONS AND TRUTH VALUES 15 2.2 LOGICAL CONNECTIVES 17 2.3 TAUTOLOGIES AND CONTRADICTIONS 31 2.4 LOGICAL IMPLICATION AND LOGICAL EQUIVALENCE 33 2.5 ARGUMENTS AND ARGUMENT FORMS 41 2.6 FORMAL PROOF OF THE VALIDITY OF ARGUMENTS 49 2.7 THE METHOD OF CONDITIONAL PROOF 57 3 PREDICATE LOGIC 63 3.1 INTRODUCTION 63 3.2 QUANTIFICATION OF PROPOSITIONAL FUNCTIONS 65 3.3 TWO-PLACE PREDICATES 71 3.4 VALIDATION OF ARGUMENTS IN PREDICATE LOGIC 79 4 AXIOM SYSTEMS AND FORMAL PROOF 89 I 4.1 INTRODUCTION 89 4.2 CASE STUDY OF A PROOF 90 4.3 AXIOM SYSTEMS 93 4.4 THEOREMS AND FORMAL PROOFS 105 4.5 INFORMAL PROOFS 116 VI CONTENTS 5 DIRECT PROOF 121 5.1 THE METHOD OF DIRECT PROOF 121 5.2 FINDING PROOFS 138 5.3 MORE ADVANCED EXAMPLES 154 6 DIRECT PROOF: VARIATIONS 167 6.1 INTRODUCTION 167 6.2 PROOF USING THE CONTRAPOSITIVE 167 6.3 PROOF BY CONTRADICTION 172 6.4 PROOF OF A BICONDITIONAL 178 7 EXISTENCE AND UNIQUENESS PROOFS 185 7.1 INTRODUCTION 185 7.2 PROOF BY CONSTRUCTION 186 7.3 NON-CONSTRUCTIVE EXISTENCE PROOFS 191 7.4 USE OF COUNTER-EXAMPLES 195 7.5 UNIQUENESS PROOFS 202 8 FURTHER PROOF TECHNIQUES 209 8.1 INTRODUCTION 209 8.2 PROOFS OF IDENTITIES 211 8.3 USE OF COUNTING ARGUMENTS 220 8.4 THE METHOD OF EXHAUSTION 232 9 MATHEMATICAL INDUCTION 239 9.1 THE PRINCIPLE OF MATHEMATICAL INDUCTION 239 9.2 THE SECOND PRINCIPLE OF MATHEMATICAL INDUCTION 256 APPENDIX: SOME DEFINITIONS AND TERMINOLOGY 265 REFERENCES AND FURTHER READING 273 HINTS AND SOLUTIONS TO SELECTED EXERCISES 275 I INDEX 313
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institution	BVB
isbn	047196199X
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spellingShingle	Garnier, Rowan Taylor, John 1957- 100 % mathematical proof Bewijstheorie gtt Logic, Symbolic and mathematical Proof theory Beweistheorie (DE-588)4145177-6 gnd
subject_GND	(DE-588)4145177-6
title	100 % mathematical proof
title_alt	Hundred % mathematical proof
title_auth	100 % mathematical proof
title_exact_search	100 % mathematical proof
title_full	100 % mathematical proof Rowan Garnier ; John Taylor
title_fullStr	100 % mathematical proof Rowan Garnier ; John Taylor
title_full_unstemmed	100 % mathematical proof Rowan Garnier ; John Taylor
title_short	100 % mathematical proof
title_sort	100 mathematical proof
topic	Bewijstheorie gtt Logic, Symbolic and mathematical Proof theory Beweistheorie (DE-588)4145177-6 gnd
topic_facet	Bewijstheorie Logic, Symbolic and mathematical Proof theory Beweistheorie
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