This is precisely the point: "eventually" never happens, no matter how long you wait. Infinity can never be reached, and so nothing can be built from infinities.
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Machine learning can go on indefinitely, though. It can keep calculating along with reality, generating deeper fractals at ever more detail. So any number you want to reach, you can calculate.
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What's the last digit of Pi?
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My point was that you can calculate to any level of detail that you like. It doesn't end, because you can always keep going. But it's still calculatable. Pi isn't really "a" number, though. It's a ratio.
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Ratios are numbers, too. Rational numbers are ratios between integers, and they can be fully known. While Pi is the ratio between circumference and diameter of a circle, it is not a rational number. You cannot calculate all of Pi.
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What do you like as a definition of "number"?
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informally, it is a subsequent labeling scheme
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Labeling what?
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whatever you want
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That sounds more like the definition of "language". :P
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Languages don't need to have subsequent labels, and numbers don't have to use compositional grammars.
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In the brain language probably does have to have relational labels, though, which probably are subsequent in some way, but they won't be 1D (linear). I think numbers are the same, though we're still mostly just using the first and second dimensional numbers, I guess.
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It seems that the representation function of linguistic labels in the brain does not preserve a transitive ordering, so I would say it is not subsequent.
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