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Proven Impossible: Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More

By (author) Dan Gusfield

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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 â€“ and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training â€“ all you need is the discipline to follow logical arguments and a pen in your hand.

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The Order of Time

Carlo Rovelli
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224 pages
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Originally published in Italian: L'ordine del tempo (Milan: Adelphi Edizioni, 2017).

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Helgoland: The Strange and Beautiful Story of Quantum Physics

Carlo Rovelli
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The Coming Wave: AI, Power and Our Future

Mustafa Suleyman
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352 pages
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