Format:
1 Online-Ressource (xiv, 254 Seiten)
ISBN:
9781009349451
Content:
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
Note:
Title from publisher's bibliographic system (viewed on 16 Feb 2024)
,
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)
Additional Edition:
Erscheint auch als Druck-Ausgabe, Hardback ISBN 978-1-009-34950-5
Additional Edition:
Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-1-009-34949-9
Language:
English
DOI:
10.1017/9781009349451
URL:
Volltext
(URL des Erstveröffentlichers)
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