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From: George Greene on 4 Jun 2010 23:40 ....that isn't computable up to that digit position". OBVIOUSLY, EVERYTHING FINITE is computable. Every uncomputable real has the property that its 1st n digits are computable, FOR ALL n. The first n digits OF ANYthing are computable. There is no limit on how big a computer can be, as long as it's finite. So any finite ANYthing is ALWAYS computable. This obviously has NOTHING WHATSOEVER TO DO with the INFINITELY many digits that are going to come AFTER whatEVER you computed up to! In other words, all natural numbers are very small (because there are only a finite number of numbers smaller than them, but an infinite number of numbers bigger than them). |