# How to prove $(\mathbb{R}\backslash \mathbb{Q})\cap (x,y)\neq \emptyset$ for $x,y\in \mathbb{R}$ and $x<y$? [duplicate]

How to prove $$(\mathbb{R}\backslash \mathbb{Q})\cap (x,y)\neq \emptyset$$ for $$x,y\in \mathbb{R}$$ and $$x?

Sorry, but I don't even know how to start. Any ideas and impulses?

## 1 Answer

Hint:

Find a nonzero rational $$r$$ such that $$x\sqrt 2