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0 (hodnocen0 x )

EB

EB

Boca Raton, Fla. : CRC Press, 2012

1 online zdroj

ISBN 9781136587597 (e-book: Mobi)

ISBN 9781136587634 (e-book: ePub)

ISBN 9781136587641 (e-book: PDF)

ISBN 9781138442061 (vázáno)

ISBN 9780415690850 (brožováno)

A Balkema book.

Obsahuje bibliografii na stranách 130-138

1. Godel, Turing -- 2. Complexity, randomness -- 3. A list of problems -- 4. The halting function and its avatars -- 5. Entropy, P vs. NP -- 6. Forays into uncharted landscapes.

Kurt Godel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory admits time machines. The Godel incompleteness phenomenon - one cannot prove nor disprove all true mathematical sentences in the usual formal mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Godel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. -- Provided by publisher..

This accessible book gives a new detailed and elementary proof of the Godel incompleteness theorems and then presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the lively historical report, the personal stories about the main character, and the writing process of this volume make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences-- Provided by publisher..

001477965

(OCoLC)778448881