Let $\Lambda$ be a non-empty subset of $\mathbb{R}_*^+$ closed under addition, with $r(\Lambda) > 0$ and $d = b - a$ as defined above. Deduce that $\Lambda \subset d\mathbb{Z}$, where $d\mathbb{Z} = \{kd \mid k \in \mathbb{Z}\}$.
Let $\Lambda$ be a non-empty subset of $\mathbb{R}_*^+$ closed under addition, with $r(\Lambda) > 0$ and $d = b - a$ as defined above. Deduce that $\Lambda \subset d\mathbb{Z}$, where $d\mathbb{Z} = \{kd \mid k \in \mathbb{Z}\}$.