Is it possible to proof with archimedes axiom that better infimum does not exist for that inequality?
$$ \frac{1+3n}{3+n^3} < \epsilon , n \in \mathbb{N}\setminus\{0\} $$
I need to transform that expression so that n is alone on one side and "all" $\epsilon$ are on the other. If the inequality shows that n is greater, then the proof is complete. However I don't know if that's possible in that case.
The problem is that n exists in 2 separate places with 2 separate powers. When it's just one variable it is easy to do the proof.