Let $[-\infty, \infty]$ be the D1275: Set of basic numbers.
The set of euclidean numbers with respect to $N \in \{ 1, 2, 3, \ldots \}$ is the D11: Set $$\begin{equation} [-\infty, \infty]^N = \prod_{n = 1}^N [-\infty, \infty] \end{equation}$$