Later lessons will develop the concept of logical reasoning and proof . First, we will present groups of axioms to help us understand the different number systems we will encounter. The terms addition, multiplication, subtraction, and division will also not be rigorously defined, but must satisfy the group and field axioms presented in Lesson 7 and lesson 13 . You were taught rudimentary algorithms in grade school which we will review very briefly. Computer scientists and some popular programming languages such as C also often treat it as a counting number.
Most books define whole numbers as the union of the counting numbers with zero.
Zero and One Indexing Zero Indexing acknowledges zero as the number we start with. One Indexing acknowledges one as the number we start with. In this class we will be flexible, but try to specify when zero indexing is to be used. The symbol N is used to denote the set of natural numbers. The set of natural numbers is an infinite set.