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Wikipedia definition
1. Simple setIn recursion theory a subset of the natural numbers is called a simple set if it is co-infinite and recursively enumerable, but every infinite subset of its complement fails to be enumerated recursively. Simple sets are examples of recursively enumerable sets, that are not recursive (--- a set is recursive if and only if both the set and its complement are recursively enumerable).
Read “Simple set” on English Wikipedia
Read “単純集合” on Japanese Wikipedia
Read “Simple set” on DBpedia

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