(related to Proposition: Unique Representation of Real Numbers as \(b\)-adic Fractions)
Every real number \(x\in\mathbb R\) can be approximated by a sequence \((q_n)_{n\in\mathbb N}\) of rational numbers \(q_n\in\mathbb Q\). More formally: For every \(x\in\mathbb R\) there is a convergent sequence of rational numbers \(q_n\in\mathbb Q\), i.e.
\[\lim_{n\rightarrow\infty} q_n=x.\]
Proofs: 1