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[Solved]: A recursively enumerable language and a recursively enumerable set

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Problem Detail: 

I am confused between these two terminologies: recursively enumerable language, recursively enumerable set.

Do they have the exactly same meaning?

Asked By : Eliza

Answered By : Hendrik Jan

No they do not have exactly the same meaning. A language is a set of strings, whereas a set can be virtually anything. Usually such a set is a set of (natural) numbers, but we also can consider sets of graphs.

However, when the sets are accepted or generated by Turing machines, then they have to be represented on a tape (for input or output). This means they have to be represented as strings anyhow. Hence for the Turing machine itself there is no difference. Only for the human beholder there is an interpretation of the string as number or graph.

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