To correctly define this, it is necessary to explain what formula_7 and formula_8 are. These are given as the even and odd real subspaces of the one-dimensional space of Grassmann numbers, which, by convention, are generated by a countably infinite number of anti-commuting variables: i.e. the one-dimensional space is given by formula_9 where "V" is infinite-dimensional. An element "z" is termed "real" if formula_10; real elements consisting of only an even number of Grassmann generators form the space formula_7 of "c-numbers", while real elements consisting of only an odd number of Grassmann generators form the space formula_8 of "a-numbers". Note that c-numbers commute, while "a-numbers" anti-commute. The spaces formula_13 and formula_14 are then defined as the "p"-fold and "q"-fold Cartesian products of formula_7 and formula_8.