Are all Recursively Enumerable languages which are not Recursive also Undecidable?
A language is recursive (newer terminology: computable, also decidable) is there is a Turing machine that always halts that recognizes the language. It is recursively enumerable (new: computably enumerable) if there is a Turing machine that accepts it (it halts and accepts for strings in the language, it might never halt for strings not in the language). If the language is not recursive, it isn't decidable (&quot;recursive&quot; and &quot;decidable&quot; are alternative terms for the same class of languages).