The homework question (for a person I'm helping in Advanced Calculus) is prove the set $A=\{x \in \mathbb{Q} \colon x < 2\}$ is a Dedekind Cut (DC).
The third property of a DC is that it does not contain a greatest element. In mathese, that's $\forall a \in A,\ \exists b \in A\ \ni b>a$.
Set $A$ meets that requirement. If you say $a=\frac{19}{10}$, then I say $b=\frac{199}{100}$; if you say $a=\frac{199}{100}$, then I say $b=\frac{1999}{1000}$, etc. But how do I write that generally, so that it's a proof?
P.S. There is no tag for advanced-calculus, so I chose calculus.
Edit: I don't need a super formal proof. It just has to be general, for homework.