The coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and
If V is the underlying vector space, and O is the origin, every point P of A is identified with the n-tuple of the components of vector OP with respect to a given basis of V.
If A is a three-dimensional space, each basis can be depicted by choosing its elements as the unit vectors of the x-axis, the y-axis, and the z-axis, respectively. In general, this will produce three axes which are not necessarily perpendicular, and where the units are set differently. Hence, Cartesian coordinates are a very special kind of affine coordinates that correspond to the case where ,,.