The authors decided to look at infinity in number, and to try to show how, throughout the course of time, men and women answered these two fundamental questions about cardinality and ordinality: how do we count? how do we order? This article is aimed at teachers of mathematics for use as a means of introducing a historical perspective into the teaching of mathematics. It also contains exercises to be solved according to ancient and modern methods. The chapter ends with a bibliography which contains, in addition to the historical sources that have been used, a certain number of books recommended for further study of the subject. (ZDM/Mathdi)