A concrete model of the real numbers (Q974760)

Let \(X\) be the set of sequences \((x_k)_{k\geq 0}\) with \(x_0\in{\mathbb Z}\) and \(x_k\in\{0,1\}\quad (k\geq 1)\). The author constructs the real numbers as equivalence classes in \(X\) and proves their basic properties.