Euclidean space

The Euclidean space of dimension $n$ refers to the set of points $(x_1, x_2, \ldots, x_n)$ , where each $x_i$ is a real number. The two-dimensional Euclidean space is the Cartesian plane, and so forth. See also coordinate geometry.

It is a metric space with respect to the distance metric, $d(\bold{x},\bold{y}) = \sqrt{(x_1-y_1)^2 + \cdots + (x_n - y_n)^2}$ .

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Euclidean space