Abstract
A theory of natural numbers will be outlined in what follows. This theory will also be extended to give an account of positive and negative integers and positive and negative rational numbers. The system of logic used will be that of Whitehead and Russell's Principia mathematica with the simple theory of types. It will be assumed that the reader is familiar with the more elementary properties of relations and with such notions as the relative product of two relations, the square of a relation, the cube of a relation, and the various other whole-number powers of relations.The guiding principle of this theory is that the natural number zero is to be regarded as the relation of the zevoth power of a relation А to А itself, and the natural number 1 is to be regarded as the relation of the first power of a relation А to А itself, and the natural number 2 is to be regarded as the relation of the square of a relation А to А itself, and so on.
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