Let $a$ and $b$ be dedekind cuts, we say that $a \prec b$,(thats $a \subsetneq b$) and
considering $0^* \prec c$( Thats mean $\exists p\in c$, $p>0$)
I want to prove that:
$ca \prec cb$
I am starting some notes on dedekind cuts and this is a proposed exercise, but sadly I have not been able to solve it. Searching on the internet I have not found this property, so I would appreciate any help :)