"Distance, or farness, is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific set of rules, and is a concrete way of describing what it means for elements of some space to be "close to" or "far away from" each other. In most cases, "distance from A to B" is interchangeable with "distance between B and A"." [Distance. Wikipedia]
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