Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge ; New York, NY
Cambridge University Press
2024
|
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/9781009349451 https://doi.org/10.1017/9781009349451 https://doi.org/10.1017/9781009349451 https://doi.org/10.1017/9781009349451 https://doi.org/10.1017/9781009349451 |
| Zusammenfassung: | In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand |
| Beschreibung: | Yes you can prove a negative! -- Bell's impossibility theorem(s) -- Enjoying Bell magic -- Arrow's (and friends') impossibility theorems -- Clustering and impossibility -- Godel-ish impossibility -- Turing undecidability and incompleteness -- Chaitin's theorem : more devastating -- Godel (for real, this time) |
| Umfang: | 1 Online-Ressource (xiv, 254 Seiten) |
| ISBN: | 9781009349451 |
| DOI: | 10.1017/9781009349451 |
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| author | Gusfield, Dan |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
| dewey-sort | 3511.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781009349451 |
| format | Electronic eBook |
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| id | DE-604.BV049728221 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-18T13:00:47Z |
| institution | BVB |
| isbn | 9781009349451 |
| language | English |
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| spelling | Gusfield, Dan Verfasser (DE-588)1175915769 aut Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more Dan Gusfield Cambridge ; New York, NY Cambridge University Press 2024 1 Online-Ressource (xiv, 254 Seiten) txt rdacontent c rdamedia cr rdacarrier Yes you can prove a negative! -- Bell's impossibility theorem(s) -- Enjoying Bell magic -- Arrow's (and friends') impossibility theorems -- Clustering and impossibility -- Godel-ish impossibility -- Turing undecidability and incompleteness -- Chaitin's theorem : more devastating -- Godel (for real, this time) In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand Proof theory Probabilities Erscheint auch als Druck-Ausgabe, Hardback 978-1-009-34950-5 Erscheint auch als Druck-Ausgabe, Paperback 978-1-009-34949-9 https://doi.org/10.1017/9781009349451 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Gusfield, Dan Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more Proof theory Probabilities |
| title | Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more |
| title_auth | Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more |
| title_exact_search | Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more |
| title_full | Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more Dan Gusfield |
| title_fullStr | Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more Dan Gusfield |
| title_full_unstemmed | Proven impossible elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more Dan Gusfield |
| title_short | Proven impossible |
| title_sort | proven impossible elementary proofs of profound impossibility from arrow bell chaitin godel turing and more |
| title_sub | elementary proofs of profound impossibility from Arrow, Bell, Chaitin, Gödel, Turing and more |
| topic | Proof theory Probabilities |
| topic_facet | Proof theory Probabilities |
| url | https://doi.org/10.1017/9781009349451 |
| work_keys_str_mv | AT gusfielddan provenimpossibleelementaryproofsofprofoundimpossibilityfromarrowbellchaitingodelturingandmore |