{"product_id":"proven-impossible-elementary-proofs-of-profound-impossibility-from-arrow-bell-chaitin-godel-turing-and-more-paperback-softback-9781009349499","title":"Proven Impossible; Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More (Paperback \/ softback) 9781009349499","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eProven Impossible\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eElementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eA highly readable presentation of elementary yet rigorous proofs of profound impossibility theorems for a broad, lay audience.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDan Gusfield (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009349499, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 18 January 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e270 pages\u003cbr\u003e23 x 15 x 1.8 cm, 0.448 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'… a great book both for the layperson and for people who know some of the material.' William Gasarch, SIGACT News\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Yes you can prove a negative!\u003cbr\u003e 2. Bell's impossibility theorem(s)\u003cbr\u003e 3. Enjoying Bell magic\u003cbr\u003e 4. Arrow's (and friends') impossibility theorems\u003cbr\u003e 5. Clustering and impossibility\u003cbr\u003e 6. Gödel-ish impossibility\u003cbr\u003e 7. Turing undecidability and incompleteness\u003cbr\u003e 8. Chaitin's theorem: More devastating\u003cbr\u003e 9. Gödel (for real, this time).\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52173726810392,"sku":"9781009349499","price":22.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009349499i.jpg?v=1781168486","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/proven-impossible-elementary-proofs-of-profound-impossibility-from-arrow-bell-chaitin-godel-turing-and-more-paperback-softback-9781009349499","provider":"Freshly Printed Books","version":"1.0","type":"link"}