How to prove $(\mathbb{R}\backslash \mathbb{Q})\cap (x,y)\neq \emptyset$ for $x,y\in \mathbb{R}$ and $x<y$?
Sorry, but I don't even know how to start. Any ideas and impulses?
2026-05-02 11:12:01.1777720321
How to prove $(\mathbb{R}\backslash \mathbb{Q})\cap (x,y)\neq \emptyset$ for $x,y\in \mathbb{R}$ and $x<y$?
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Hint:
Find a nonzero rational $r$ such that $x\sqrt 2<r<y\sqrt2$