不完备性

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• More specifically, Einstein's and Gödel's meta convictions were addressed to the question of whether their respective fields are descriptions of an objective reality--existing independent of our thinking of it--or, rather, are subjective human projection, socially shared intellectual constructs. (查看原文)

  辰 2013-08-04 14:18:32

• The first of these problem revolving around Cantor's continuum hypothesis. What is Cantor's continuum hypothesis? The great nineteenth-century mathematician Georg Cantor had proved that (roughly speaking) there are more real numbers than there are natural numbers, even though there are an infinite number of both. Cantor showed, by means of an elegant argument called the "diagonal argument", that in the infinite pairing of one natural number with one real number, every natural number will be paired with a real number but some real number or other will forever be left out. The set of real numbers is thus of a higher ordinality (roughly speaking, there are more of them) than the set of natural numbers. Cantor hypothesized that there is no infinite set that intervenes between the set of natura... (查看原文)

  辰 2013-08-05 10:25:43

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