If a given element is homogeneous of a grade "k", then it is a "k"-vector, but not necessarily a "k"-blade. Such an element is a "k"-blade when it can be expressed as the exterior product of "k" vectors. A geometric algebra generated by a 4-dimensional vector space illustrates the point with an example: The sum of any two blades with one taken from the XY-plane and the other taken from the ZW-plane will form a 2-vector that is not a 2-blade. In a geometric algebra generated by a vector space of dimension 2 or 3, all sums of 2-blades may be written as a single 2-blade.