Find infimum of $\{\frac{1}{n^2} | n \in \Bbb N\}$ in $\mathbb{R}$

So I need to find the infimum of$\{\frac{1}{n^2} | n \in \Bbb N\}$

I know that this means that I need to find some $x$ where $x < \frac{1}{n^2} \forall n \in \Bbb N$.

By intuition I know that $\lim_{n \to \infty}$, is $0$, which means that the infimum should be $0$, but is there a more formal way of proving that without using limits?