individual elements or points of the exterior algebra generated by a set of Grassmann variables or Grassmann directions or supercharges

Grassmann numbers are individual elements or points of the exterior algebra generated by a set of Grassmann variables or Grassmann directions or supercharges , with possibly being infinite.

with possibly being infinite

Grassmann numbers are individual elements or points of the exterior algebra generated by a set of Grassmann variables or Grassmann directions or supercharges , with possibly being infinite.

elements of the exterior algebra

So, the Grassmann numbers are elements of the exterior algebra, and the Clifford algebra has an isomorphism to the exterior algebra, but the exterior algebra's relation to the orthogonal group and the spin group, used to construct the spin representations, give the exterior algebra a deep geometric significance.

a sort of classical limit of anticommuting operators in Hilbert space

The problem is that if the Grassmann numbers are indeed a sort of classical limit of anticommuting operators in Hilbert space, then the limit $\hbar\rightarrow0$ itself does not make any sense from a physical point of view since in this limit $\hbar\rightarrow0$, the spin observables vanish totally and what we obtain then would be a $0$, which is a trivial theory.

anti-commuting numbers

Grassmann numbers are anti-commuting numbers, so that x times y = –y times x.

by convention over the complex numbers

Thus, by convention, the Grassmann numbers are usually defined over the complex numbers.

the $c$-numbers for fermionic creation or annihilation operators in the same way as the ordinary commuting $c$-numbers are the numbers for the ordinary bosonic creation or annihilation operators (and many other operators)

The Grassmann numbers are the $c$-numbers for fermionic creation or annihilation operators in the same way as the ordinary commuting $c$-numbers are the numbers for the ordinary bosonic creation or annihilation operators (and many other operators).

or objects

Grassmann numbers are generated by anti-commuting elements or objects.

by anti-commuting elements

Grassmann numbers are generated by anti-commuting elements or objects.

anticommuting numbers (also called Grassmann numbers

We will define anticommuting numbers (also called Grassmann numbers) by giving algebraic rules for manipulating them.

Coleman Mandula

Coleman Mandula are Grassmann numbers valued in the algebra, and A is their algebraic index, corresponding, ultimately, to the basis elements, T_A, of e8.

the exterior algebra of anti-commuting numbers,

Depending on the context, supercharges may also be called Grassmann variables or Grassmann directions; they are generators of the exterior algebra of anti-commuting numbers, the Grassmann numbers.