Example 1

Tag 0C2D, permanent. Cite it as [Bourbaki, Tag 0C2D].

The Euclidean distance $d(x, y)$ (Chapter VI, § 2, no. 1) is a metric on real $n$ -dimensional number space $\mathbf{R}^n$ ; so are the functions

\sup_{1 \leq i \leq n} |x_i - y_i| \quad \text{and} \quad \sum_{i=1}^n |x_i - y_i|.

All these metrics are equivalent ( $\S$ 1, no. 2).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.