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}