Ciro Santilli
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Is a decision problem of determining if something belongs to a non-recursive language.
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Or in other words: there is no Turing machine that always halts for every input with the yes/no output.
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Every undecidable problem must obviously have an infinite number of "possibilities of stuff you can try": if there is only a finite number, then you can brute-force it.
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Some undecidable problems are of recursively enumerable language, e.g. the halting problem.
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Coolest ones besides the obvious boring halting problem:
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Ancestors

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