I have a problem with the following question on Dedekind's cut.
Is the set $\{t\in \mathbb{Q}: -t\not\in r\}$, where $r$ is a real number (a cut), a Dedekind cut? Why or why not?
The definition of Dedekind's cut here is: nonempty, not $\mathbb{Q}$, contains all rational number smaller than it, and does not contain a largest element.
Thank you.