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