Producer of Dedekind Cut/Examples

Examples of Producers of Dedekind Cuts

Example: 2

Let $L = \set {l \in \Q: l \le 2}$ and $R = \set {r \in \Q: 2 < r}$.

Then $\tuple {L, R}$ is a dedekind cut of $\Q$, and $2$ is a producer of $\tuple {L, R}$

Example: $\sqrt2$

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 $\tuple {L, R}$.