100 % mathematical proof:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 317 S. Ill., graph. Darst. |
| ISBN: | 047196199X |
Staff View
MARC
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Record in the Search Index
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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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| building | Verbundindex |
| bvnumber | BV010995526 |
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| callnumber-label | QA9 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)35208402 (DE-599)BVBBV010995526 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:19Z |
| institution | BVB |
| isbn | 047196199X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007360178 |
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| physical | VIII, 317 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Wiley |
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| spelling | Garnier, Rowan Verfasser aut 100 % mathematical proof Rowan Garnier ; John Taylor Hundred % mathematical proof Chichester [u.a.] Wiley 1996 VIII, 317 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bewijstheorie gtt Logic, Symbolic and mathematical Proof theory Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s DE-604 Taylor, John 1957- Verfasser (DE-588)141968737 aut GBV Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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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