Are there any countable sets that are not computably enumerable?
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04-11-2019 - |
문제
A set is countable if it has a bijection with the natural numbers, and is computably enumerable (c.e.) if there exists an algorithm that enumerates its members.
Any non-finite computably enumerable set must be countable since we can construct a bijection from the enumeration.
Are there any examples of countable sets that are not computably enumerable? That is, a bijection between this set and the natural numbers exists, but there is no algorithm that can compute this bijection.
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