Question

Small math question:

Answer 1

Let x,y \(\in \mathbb{R} / x<y\) prove that the following affirmations are true:
(1) In the density of \(\mathbb{Q} \) in \(\mathbb{R} \) there exists \(a \in \mathbb{Q} \) such that \(x<a<y\)
(2) In the density \(\mathbb{R} / \mathbb{Q} \) in \(\mathbb{R} \) there exists \(\alpha \in \mathbb{R} / \mathbb{Q} \) such that \(x< \alpha < y\)