Dedekind cut for 1/x

Question

I’m kind of new to this concept and trying to get my head over it.

How do you construct a dedekind cut for $\frac{1}{x}$ where $x$ is a positive real number?

Answer 1

$\newcommand{\Q}{\mathbb{Q}}$ A Dedekind cut is a partition of $\Q$ satisfying certain additional nice properties. So, one way you could do this (somewhat trivially) is by taking $A = \{a \in \Q \mid a < \frac{1}{x} \}$ and $B = \{b \in \Q \mid b \geq \frac{1}{x} \}$. Of course, this relies on the assumption that you already have $x$ defined.