The real numbers line isn't countable.
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Yes, there are only integer values. Everything else is a function, not a value.
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So you disagree that learnability and generalization are similar to the continuum hypothesis because data sets are finite and countable?
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The operations we perform during machine learning are all based on finite automata. A theory that is admitting more than that is describing a different universe than machine learning.
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language and math also lives there.
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I don't believe I've observed or read anything that suggests (convincingly) that there is some material reality that is not discretely quantized. The alternative appears to me to be a fantasy of romanticized, possibly completely unreal, mathematical lore.
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Do I get this correctly? We cannot ever say whether a learning set has been big enough to make further predictions with a given probability P for any P?
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