Let $x_1, x_2, x_3, \ldots \in \mathbb{Q}$ each be a D994: Rational number such that

(i)	\begin{equation} x_n = \frac{1}{n} \end{equation}

Let $\varepsilon > 0$ and choose $n$ such that $n > 1 / \varepsilon$. Then \begin{equation} \begin{split} \left| \frac{1}{n} \right| = \frac{1}{n} < \varepsilon \end{split} \end{equation} Since $\varepsilon > 0$ was arbitrary, the claim follows due to R1089: Characterisation of convergent sequences in metric space. $\square$