Zu jeder rationalen Zahl q ∈ Q {\displaystyle {}q\in \mathbb {Q} } sei ein Intervall [ a q , b q ] {\displaystyle {}[a_{q},b_{q}]} derart gegeben, dass q {\displaystyle {}q} in dessen Innern liegt, also q ∈ ] a q , b q [ {\displaystyle {}q\in {]a_{q},b_{q}[}} . Ist
![{\displaystyle {}[a_{q},b_{q}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/acf90053fb7f7392629381ce862e50d8f6507fb8)
![{\displaystyle {}q\in {]a_{q},b_{q}[}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/98baf7a240a488665c99e77321bcea5742cf1858)
![{\displaystyle {}\bigcup _{q\in \mathbb {Q} }[a_{q},b_{q}]=\mathbb {R} \,?}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bea90bc9999cca5982e0a1fcf5fa01c054dd99d6)