Assume for every real number $x$, there is an integer $N$ such that $N>x^3$. Prove that for every positive real number $\epsilon$, there exists a positive integer $N$ such that for all $n\geq N$, $\frac{1}{n}<\epsilon$
Ok so I know I am suppose to show an attempt or at least explain my thought process, but honestly I don't even know how to start this proof. Any suggestions?