How can I prove or disprove that every countable union of recursive sets is recursive?
What about recursive enumerable (r.e.)? How can I prove or disprove that every countable union of r.e. sets is r.e.?
Please help me, I really appreciate it.
2026-04-06 20:42:00.1775508120
Prove or disprove: every countable union of recursive sets is recursive.
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Take your favourite non-recursively enumerable set of natural numbers. It is countable. It is therefore a countable union of singletons, each containing one number. Singletons are r.e. and recursive. So ....