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A coordinate space is a space in which an ordered list of coordinates, each from a set (not necessarily the same set), collectively determine an element (or point) of the space – in short, a space with a coordinate system.

A coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring.

This article incorporates text from Wikipedia:Coordinate space and Wikipedia:Coordinate system.