Notes on Russell's theory of number

Abstract

This paper treats the development of the real number system. As the title suggests, it is based on the theory of number as presented by Bertrand Russell in his two works, the "Introduction to Mathematical Philosophy" and the "Principles of Mathematics". My chief aim has been to reduce the concept of 'number' to such logical concepts as 'class' and 'relations'. The first part of this paper deals with these concepts and the latter parts with their applications to 'number'. Regarding the operations between numbers, much is left undone. I merely offer the essential definitions. Certain refinements of these operations, such as the associative and distributive laws of algebra, are omitted. These omissions are not due to the fact that such laws are unimportant or that they cannot be derived from 'number' as defined in this paper, but to the fact that I discuss here only the essential features of the number system and not the various laws which may be deduced from these.