recursively enumerable languages

Question

if L1,L2,.... are any recursively enumerable subsets of Σ*, then the union of Li's is Recursive enumerable.

whether the above statement is true or false?

Comments

true. RE sets closed under union

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but here the question is asking about infinite union. so is the property true for infinite union too?

because, regular is also closed under union but not under infinite union

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only regular is not closed under infinite union

Answer 1

It's TRUE, https://www.geeksforgeeks.org/recursive-and-recursive-enumerable-languages/