ABSTRACT

When we introduced natural numbers, we were motivated by the need to formalize the process of "counting": the natural numbers start with 0 and are generated by successively increasing the number by one unit: 0, 1, 2, 3, … , and so on. We defined the operation of successor by S(x) = x U {x} and introduced natural numbers as elements of the smallest set containing 0 and closed under S.