The spin group Spin(V) is defined to be the subgroup of Cleven(V) consisting of multivectors R such that  That is, it consists of multivectors that can be written as a product of an even number of unit vectors.
The spin group Spin(V) is identified as a subset of Cleven(V) containing multivectors R for which  applies. These multivectors consist of products involving an even count of unit vectors.