Yes, the theorem works in finite fields, according to wikipedia (Why fields, when a ring is enough? We're not dividing anything.)
I am saying that the only case you really need a potentially unbound integer is when you're counting objects (or their obvervations, or the instances of their models), but the magnitude of the count is limited by the Universe. Maybe is some other Universe you'd need 1000-bit numbers, but not in this one. All other uses of "integer numbers" in speech are for the sake of word economy and convenience. Are a 250 Gb hard drive contents an integer? One can say so, but then they can represent a rational number in [0, 1) just as well. So unless a bit vector is really used as an integer - for object counting - there is no particular reason not to say it's a rational in [0, 1), and who's to say which way is "right"?
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timeasmymeasure
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Date: 2006-10-28 04:40 am (UTC)I am saying that the only case you really need a potentially unbound integer is when you're counting objects (or their obvervations, or the instances of their models), but the magnitude of the count is limited by the Universe. Maybe is some other Universe you'd need 1000-bit numbers, but not in this one. All other uses of "integer numbers" in speech are for the sake of word economy and convenience. Are a 250 Gb hard drive contents an integer? One can say so, but then they can represent a rational number in [0, 1) just as well. So unless a bit vector is really used as an integer - for object counting - there is no particular reason not to say it's a rational in [0, 1), and who's to say which way is "right"?