# Need help understanding what co-recursively enumerable means

Lets say I have a set: $$L = \{\langle G \rangle | L(G) = \sum^{\star}\}$$ and the question asks if it is co-RE. I know that if something is co-RE, it halts on every input not in L but may or may not halt on inputs in L.

So in this case would something "not in L" be nothing?

• What is "co-CE"? Or is it a typo? Also, is $G$ supposed to be a TM here? – dkaeae Dec 17 '18 at 7:12

No. A string $$\langle G\rangle$$ is not in $$L$$ means $$L(G)\ne \Sigma^*$$. Such strings exist of course. For example, if $$G$$ is a machine that rejects anything, then $$L(G)=\emptyset$$, thus $$\langle G\rangle\notin L$$.