The most elementary mathematical objects are, no doubt, the natural numbers. In this chapter, we use mathematical induction to construct the natural numbers in the ﬁrst place. Thanks to this inductive (or recursive) nature, elementary arithmetic operations such as addition and multiplication can also be deﬁned recursively. The conclusion is, thus, that the sum of two natural numbers is a natural number as well, and that the product of two natural numbers is a natural number as well. In other words, the set of natural numbers is closed under addition and multiplication.