Let $\mathbb{R}^N$ be a D1256: Euclidean real vector space.
Let $|\cdot| : \mathbb{R} \to [0, \infty)$ be the D412: Absolute value function.
The euclidean distance function on $\mathbb{R}^N$ is the D4367: Unsigned real function \begin{equation} \mathbb{R}^N \times \mathbb{R}^N \to [0, \infty), \quad (x, y) \mapsto \left( \sum_{n = 1}^N |x_n - y_n|^2 \right)^{1/2} \end{equation}