I don't understand a difference between REC and RE languages.
1- Since the set of RE languages is larger than that of REC languages, i.e., REC is a subset of RE, what are the languages that differentiate these two? In RE\REC, there are languages that don't halt always. If this is correct, what can be an example of such a language? Are the strings in a language RE\REC only those for which computation may not end, or are there also strings for which computation ends?
2-If I understand correctly, a REC language halts all input strings, both in the language and not in the language. I'm not clear on an example of a string not in the language that is then computed and why, even if it's not in the language, it is computed.