2. There is an important difference between $\mathbb{Q}$ and $\mathbb{R}$ that allows you to find initial segments of $\mathbb{Q}$ you cannot write $\{x\in\mathbb{Q}\ ;\ x for any $a\in \mathbb{Q}$.
An example different from the ones you get with the remark: $[-\infty ,0]\subset\mathbb{R}$.