More complicated numbers systems with generalizations of this type of multiplication in 4 and 8 dimensions can be defined. Kervaire (1958) and Bott & Milnor (1958) independently proved that the only four division algebras built on the reals are \(\mathbb{R}\), \(\mathbb{C}\), \(\mathbb{H}\) and \(\mathbb{O}\), so the table gives a comprehensive view of all possible algebra’s that define a notion of extensiveness. For each of the number classes in the table a separate theory of information me