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  "body": "\n## Summary\n\nA computable set, also called a recursive or decidable set, is a set of natural numbers for which an algorithm decides membership.\nThe algorithm must halt on every input and answer yes or no correctly.\nComputable sets are exactly the sets whose characteristic function is a total [[computable function|KZSB5E471K]].\nThey are the bottom level of the hierarchies of complexity of sets in [[computability theory|X14Y880PN5]].\n\n## Explanations\n\n### L1 human\n\nA set of numbers is computable if a program can always answer the question \"is $n$ in the set?\" in finitely many steps.\nThe even numbers and the prime numbers are computable sets.\nThe set of numbers of programs that halt is not computable, although a program can confirm membership when it holds.\nEach finite set is computable, since a program can simply contain the list.\n",
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