# Metric (mathematics)

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In mathematics a set is said to have a **metric** if there is a notion of distance on the set that fits our intuition about how distance should behave. More formally, an operation on a set **A** to the real numbers is said to be a metric if for all and , we have the following three properties.

- and this equality is strict if and only iff

Intuitively, property 1 says that distance cannot be negative and two elements of the set are zero distance away from each other if and only if they are the same element. Property 2 says that the distance from x to y is the same as the distance from y to x. Property three says that the distance going from x to y to z is at least the distance to go from x to z. This third property is known as the "triangle inequality."