## Idea ## The real numbers as encountered in pre-algebra. ## Definition ## The __pre-algebra real numbers__ $\mathbb{R}$ is an [[Archimedean ordered field]] such that the [[infinite decimal representation of a unit interval|infinite decimal representation]] function of the [[unit interval]] $\mathcal{I}:[0, 1]_\mathbb{R} \to (\mathbb{N} \to [0, 9]_\mathbb{N})$ is an [[equivalence]]. ## See also ## * [[real numbers]]