Prove that the empty set has outer measure zero verification

Question

$\forall sets A, m^*(A) \geq 0 $

Since $m^*(\{x\})=0$ where $\{x\}$ is any singleton

and the empty set is a subset of every set

$0 \leq m^*(\emptyset) \leq m^*(\{x\})$.

Hence

$m^*(\emptyset)=0$

QED?