 The operation of multiplication with the associated logarithmic function characterizes our intuitions about additivity of the concept of information exactly. It leads to a natural bijection between the set of natural numbers \(\mathbb{N}\) and the set of multisets of numbers (i.e., sets of prime factors). The notion of a multiset is associated with the properties of commutativity and associativity. This program can be extended to other classes of numbers when we study division algebras in higher dimensions. The following table gives an overview of some relevant number classes together with the properties of the operation of multiplication for these classes: 