Let $\mathbb{Q}$ be the D368: Set of rational numbers.
The set of basic real numbers is the D11: Set
\begin{equation}
\mathbb{R}
: = \{ x : x \text{ is Dedekind cut in } \mathbb{Q} \}
\end{equation}
▶ | D1275: Set of basic numbers |
▶ | D370: Set of irrational numbers |
▶ | R4483: Real number is zero iff equal to its reflection |