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In geometry, a point is a unique entity in space. It is considered zero-dimensional and has no length, width or height.
It is predefined in geometry but may be defined as the intersection of two non-parallel lines in a 2D plane. In the Cartesian coordinate plane, a point can be defined by an ordered pair with an x- and y-coordinate. In the thre euiclidean space a point is characterized by a triplet of numbers. In the four-space by four dumbers.
In the more abstract sense a point is an element of some set, X, and depending of this ambient set, a point could be as explained earlier of a point could be a vector in a vectorspace, or a function between two set, a matrix representing a linear transformation intra two vectorspaces.