# Difference between revisions of "Metric (mathematics)"

From Conservapedia

(stub) |
|||

Line 7: | Line 7: | ||

Intuitively property 1 says that distance cannot be negative and two points are zero distance away from each other if and only if they | Intuitively property 1 says that distance cannot be negative and two points are zero distance away from each other if and only if they | ||

are in fact that the same . 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. | are in fact that the same . 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. | ||

+ | |||

+ | [[Category:Mathematics]] |

## Revision as of 04:33, 11 March 2007

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 points are zero distance away from each other if and only if they are in fact that the same . 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.