Let $\mathbb{R}$ be the D282: Set of real numbers.
The set of euclidean real numbers with respect to $N \in 1, 2, 3, \ldots$ is the D11: Set \begin{equation} \mathbb{R}^N = \prod_{n = 1}^N \mathbb{R} = \{ x \mid x : \{ 1, \ldots, N \} \to \mathbb{R} \} \end{equation}