I have read the Wikipedia article on Recursively Enumerable languages. The article suggests that the halting problem is recursively enumerable but undecidable. My idea till today was that the halting problem belongs to a class of languages which are not even recursively enumerable. But the article suggests that the halting problem is recursively enumerable. My doubt is about the relationship between undecidable problems and recursively enumerable languages. Are all undecidable problems recursively enumerable languages?
If there is a problem which belongs to the class of non recursively enumerable languages, will it be always undecidable?
Also could any one suggest a problem which is not even recursively enumerable?