In this tutorial, we look at sets, basic operations on sets, and inequalities (like a < b). The set of all positive real numbers is used to define inequalities of real numbers, and rules of inequalities are used to solve inequalities involving an unknown variable.

Proofs of the rules of inequalities are given for advanced students, but they can easily be omitted by ordinary students. The proofs rely on the existence of the set of all positive real numbers (and their properties) which we take as an axiom (assumed true), but this set can be constructed in advanced Set Theory.