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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.

  • 0
    What have you tried? About which property of a Dedekind cut are you unsure here?2012-09-30
  • 2
    Hint: What if $r$ is rational?2012-09-30

2 Answers 2