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The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance.
The Euclidean distance is the prototypical example of the distance in a metric space, [10] and obeys all the defining properties of a metric space: [11] It is symmetric, meaning that for all points and , (,) = (,). That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is ...
For example, d(1, {3,6}) = 2 and d(7 ... among all isometries I of the metric space M to itself. This distance measures how far the shapes X and Y are from being ...
For example, psychological distance is "the different ways in which an object might be removed from" the self along dimensions such as "time, space, social distance, and hypotheticality". [5] In sociology , social distance describes the separation between individuals or social groups in society along dimensions such as social class , race ...
A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...
In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space. It is named after Leonid Vaseršteĭn .
In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L ∞ metric [1] is a metric defined on a real coordinate space where the distance between two points is the greatest of their differences along any coordinate dimension. [2] It is named after Pafnuty Chebyshev.
Define the distance between two different words to be 2 −n, where n is the first place at which the words differ. The resulting metric is an ultrametric. The set of words with glued ends of the length n over some alphabet Σ is an ultrametric space with respect to the p-close distance.