Show $\forall \delta > 0, \exists n \in \mathbb{N}$ such that $\frac{1}{n} < \delta$ The question is in the title, but I have no idea how to solve it, so a few hints would be appreciated, thanks.

Given $\delta$, let $k = \frac{1}{\delta}$
$$\delta = \frac{1}{\frac{1}{\delta}} = \frac{1}{k}$$
Consider $ \frac{1}{\lfloor k+1 \rfloor}$.
