Let $L_1$ be some language in $R$. Let $L_2$ be some language in $RE$. Is it necessarily that $L_1 \leq_m L_2$ ? I know that for non trivial $L_1$,$L_1$ in $R$ it is right to say that $L_1 \leq_m L_2$. But I can't prove the first case.
and another question: I am almost certain that the following is true, though I have not found any reference to it on the Internet: The identity function is a mapping reduction from $\emptyset$ to $\emptyset$.