Before starting the development of the natural number system a few concepts, beginning with binary operations, need to be explored.
The operations of addition and multiplication are examples of binary operations on certain sets of numbers. Union and intersection of sets are also binary operations on the power set of a set. In general, a binary operation may be applied to a pair of elements from a set. The result of that application is a unique element in that set. If this sounds like a function is involved, it is.