enumerability造句

I don't understand what do you mean about recursive enumerability of a " language "?
It is an open question to give supports for a " Church thesis " for fuzzy mathematics, the proposed notion of recursive enumerability for fuzzy subsets is the adequate one.
In the article about Matiyasevich's theorem it says, " Some recursively enumerable sets are non-recursive . " Recursively enumerable means that an algorithm exists that halts if and only if integer n is a member of recursively enumerable set S . But non-recursive means that there isn't an algorithm that can " output a correct yes-or-no answer to the question of whether n is a member of S . " Maybe I'm missing something here, but doesn't recursive enumerability imply recursiveness?
It's difficult to find enumerability in a sentence. 用enumerability造句挺难的