Show that $\alpha$ has degree 1 if and only if $\alpha \in \mathbb { Q }$, where the degree of $\alpha$ is the degree of its minimal polynomial $\Pi_{\alpha}$.
Show that $\alpha$ has degree 1 if and only if $\alpha \in \mathbb { Q }$, where the degree of $\alpha$ is the degree of its minimal polynomial $\Pi_{\alpha}$.