Let's give a bijection between $ \{ x \in \mathbb{R}: 2 \ge x \ge 1 \} $ and $\mathbb{R} $

Question

Can I maybe use in some way Hilbert's Grand Hotel Paradox or in which way can I find such a bijection?

Answer 1

$\Bbb{R}$ bijects with $(0,1)$ via a scaled and translated $\tan$ function, so you're effectively looking for a bijection between $[0,1]$ and $(0,1)$. See Bijection between an open and a closed interval.