Euclidean -space,
sometimes called Cartesian space or simply -space, is the space of all n-tuples
of real numbers, (, , ..., ). Such -tuples are sometimes called points,
although other nomenclature may be used (see below). The totality of -space is commonly denoted , although older literature uses the symbol (or actually, its non-doublestruck
variant ;
O'Neill 1966, p. 3).
-space,
sometimes called Cartesian space or simply 
-space, is the space of all n-tuples
of real numbers, (
, 
, ..., 
). Such 
-tuples are sometimes called points,
although other nomenclature may be used (see below). The totality of 
-space is commonly denoted 
, although older literature uses the symbol 
(or actually, its non-doublestruck
variant 
;
O'Neill 1966, p. 3).
is a vector
space and has Lebesgue covering dimension 
. For this reason, elements of 
are sometimes called 
-vectors. 
is the set of real numbers
(i.e., the real line), and 
is called the Euclidean plane.
In Euclidean space, covariant and contravariant
quantities are equivalent so 
.
