Question about the set of all non-recursively enumerable languages

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Is the set of all non-recursively enumerable languages uncountable or countable? Proof? (I would assume it is uncountable but not sure.)

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HINT: There are uncountably many languages total, and only countably many r.e. languages, so . . .

(More generally, it's a good rule of thumb that "most" languages aren't "simple".)