| 41. | The resulting mathematical theory is called computable analysis.
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| 42. | Then there are computable functions f \ in F and g \ notin F.
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| 43. | The only assumption is that the environment follows some unknown but computable probability distribution.
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| 44. | The list of undecidable problems gives additional examples of problems with no computable solution.
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| 45. | Not every set of natural numbers is computable.
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| 46. | The image of a computable set under a nondecreasing total computable function is computable.
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| 47. | The image of a computable set under a nondecreasing total computable function is computable.
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| 48. | The image of a computable set under a nondecreasing total computable function is computable.
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| 49. | Moreover, any computable set of numbers can be defined by some arithmetical formula.
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| 50. | Zeno machines allow some functions to be computed that are not Turing-computable.
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