chapter  15
9 Pages

Nearly All Numbers are Insane

WithMalcolm E Lines

In the previous chapter we sketched the manner in which the system of arithmetic for the counting numbers could be built up from a set of simple axioms, or ‘self-evident’ truths, and developed from these initial concepts in a logical fashion. We must now confront the problem that this set of natural numbers is not always sufficient to enable us to carry out all the operations of arithmetic (like addition, subtraction, multiplication and division) which have been defined. In order to make our number system as useful and self-contained as possible, while still retaining its logical consistency, it therefore becomes necessary to gradually expand the meaning of number itself.