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Otherwise, if all the elements in a set can be represented by a at most n symbols (finite Kolmogorov complexity), I could count them by creating a n dimensional pairing function. Or atleast, that is my assumption. Any thoughts? Edit: as @Carl has pointed out the correct term for sequences that have no finite representation is Kolmogorov Random not infinite as I used in my title. |
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Do all uncountable sets contain elements with infinite Kolmogorov complexity?Otherwise, if all the elements in a set can be represented by a at most n symbols (finite Kolmogorov complexity), I could count them by creating a n dimensional pairing function. Or atleast, that is my assumption. Any thoughts?
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