# metric space

In mathematics, a metric space consists of a set , the “*space*,” for which the distance between all of it’s members can be calculated using a function , the *metric*.

must be a real function defined on , and for each the following must all be true:

- and (non-negative, identity of indiscernibles)
- (symmetry)
- (triangle inequality)

is also known as the *distance function* or just *distance*.

The most common metric space is 3-dimensional Euclidean space.

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