a blade’s grade is the number of basis vectors that are multiplied together (after it is reduced)
the geometric product of >𝑛 vectors can always be reduced to a geometric product with ≤𝑛 vectors, where 𝑛 is the dimension of the associated vector space
a blade of grade k is called a k-blade
permutations of the same product end up being scaled versions of each other, so it is possible to define a set of blades as a basis for the vector space of multivectors by choosing one of each permutation set
the standard basis of ℝ3 {𝑒1, 𝑒2, 𝑒3} leads to this standard basis of blades for 𝔾3 {1, 𝑒1, 𝑒2, 𝑒3, 𝑒1𝑒2, 𝑒1𝑒3, 𝑒2𝑒3, 𝑒1𝑒2𝑒3}