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by FabHK
3358 days ago
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All books written and will be written (in finite time) - yes, rational. All possible questions (infinitely many) - no, that would be a non-terminating non-periodic binary, right. From the article: > 2.4 Borel’s know-it-all number > The idea of being able to list or enumerate all possible texts in a language is an extremely powerful one, and it was exploited by Borel in 1927 [Tasi ́c, 2001, Borel, 1950] in order to define a real number that can answer every possible yes/no question! > You simply write this real in binary, and use the nth bit of its binary expansion to answer the nth question in French. > Borel speaks about this real number ironically. He insinuates that it’s illegitimate, unnatural, artificial, and that it’s an “unreal” real number, one that there is no reason to believe in. |
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