Universal computation is the set of all computable functions that can compute the set of all computable functions.
No, it really just a friendly set of computable functions, like the Turing Machine or the Python interpreter or the Game of Life.
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Computable functions in a finite amount of time? Or just computable functions without worrying whether the machine will halt or not ?
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A function that cannot be computed in a finite amount of time is not computable.
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