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 Not only would it be cool but the mental image of Dave's suffering when he writes a message in unintelligible characters makes me grin uncontrollably. - Andrew Schreiber [more] |
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#28
15-03-2006, 08:21
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Re: I know pi
Quote:
Take the string .d1d2d3d4d5d6d7d8d9d10d11... where the di are digits in whatever base you like. The set of these is R restricted to [0,1]. There exists the following injective (one-to-one) map: .d1d2d3d4d5...|--.d1d2d2d3d3d3d4d4d4d4d5d5d5d5d5... The image of this map cannot have cardinality smaller than R, so it cannot be contained in the rationals. Therefore, there exists some irrational number .d1d2d2d3d3d3d4d4d4d4... 
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