What Is a Number?

In Chap. 1 , we used addition and multiplication of the natural numbers to introduce first-order logic. Now, equipped with formal logic, we will go back to reconstruct the natural numbers and other number systems that are built on them. The set of natural numbers with a set of two relations—addition and multiplication—is a fundamental mathematical structure. In the previous discussion, we took the structure of natural numbers for granted, and we saw how some of its features can be described using first-order logic. Now we will examine the notion of natural number more carefully. It will not be as easy as one could expect.