Number Systems

Giuseppe Peano’s axioms for the natural numbers are as follows. In this discussion, we will follow tradition and use the notation 0 to denote the “successor” of a natural number. For instance, the successor of 2 is 20. Intuitively, the successor of n is the number nC 1. However addition is something that comes later; so we formulate the basic properties of the

natural numbers in terms of the successor function.