# Reduction of $RE$ language

Suppose that the language $$L_1$$ reduces to the language $$L_2$$ in polynomial time, $$L_1\leq_p L_2$$. If $$L_2$$ is recursive enumerable then so is $$L_1$$, but why isn't $$L_1$$ recursive? Because $$L_2$$ is at least as hard as $$L_1$$, and so $$L_1$$ could be easier than $$L_2$$. Why isn't $$L_1$$ recursive? Explain with an example.

Every language reduces to itself. Take $$L_1 = L_2$$ to be any recursively enumerable language which isn't recursive.