Gödel ´s Proof
Gödel ´s Proof
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This book, now revised, expanded and updated, is the first book to present a readable explanation of the main ideas and broad implications of Gödel´s proof.
Gödel´s incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman´s original text was one of the first (and best) to bring Gödel´s ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel´s theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel´s solution so dense as to be nearly indigestible.
Gödel´s incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman´s original text was one of the first (and best) to bring Gödel´s ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel´s theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel´s solution so dense as to be nearly indigestible.
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