Producer of Dedekind Cut/Examples/sqrt2

Example of Producer of Dedekind Cut
Let $L = \set {l \in \Q: l < \sqrt 2}$ and $R = \set {r \in \Q: \sqrt 2 < r}$.

Then $\tuple {L, R}$ is a Dedekind cut of $\Q$, and $\sqrt 2 \notin \Q$ is a producer of $\tuple {L, R}$.