Definition:Euclidean Metric/Real Vector Space

Consider the Euclidean space $$\left\{{\reals^n, d}\right\}$$.

The metric $$d$$ on such a space, defined as $$d \left({x, y}\right) = \left({\sum_{i=1}^n \left({x_i - y_i}\right)^2}\right)^{1 / 2}$$, is called the Euclidean metric.