Show that the order of any element $g \in G$ divides $n$, where $n$ is the order of a group $G$.
So far I have shown that: $G$ - finite group and let $g \in G$, therefore, the order of the subgroup generated by $g$ equals the order of $g$. Using Lagrange's Theorem we get that the order of $g$ divides $n$, which we had to prove. Is this a valid proof or am I missing something? Any ideas?
