Turing machine and Recursive Language

Question

If total turing machine is a proper subset of turing machine then why recursive language is not a proper subset of Recursive Enumerable ?

Comments

(Source: geeks for geeks)

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bro, if some language is in Recursive, then it should also come in recursively enumerable. this comes from their definition. Intuitively, any language for which a TM is present is recursively enumerable. in that way, the set of recursive languages is also RE. Is this what you asked in question? that geeksforgeeks says R is a subset of RE, well it is proper subset also.

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it is proper subset not subset

Answer 1

1. there are some language which are RE but not RECURSIVE so definitely R is proper subset of RE

Answer 2

recursive  language is proper subset of recursive Enumerable  language . look at the chomsky hierarchy.