The coordinates representing any point of an 
-dimensional affine space 
by an 
-tuple of real numbers, thus establishing a one-to-one
correspondence between 
and 
.
If 
is the underlying vector space, and 
is the origin, every point 
of 
is identified with the 
-tuple of the components 
of vector 
with respect to a given basis 
of 
.
If 
is a three-dimensional space, each basis 
can be depicted by choosing its elements as the
unit vectors of the 
-axis,
the 
-axis,
and the 
-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 
,
,
.
