The main aim of the article under review is to introduce some notions of elementary mathematics via the theory of binary relations and quotient sets. The author uses the viewpoint of naive set theory for introducing the inclusion relation as well as \(\cup\), \(\cap\), and the Cartesian product for sets. The notion of a binary relation is introduced and some special cases are discussed; in particular, the notions of reflexive, symmetric, antisymmetric, transitive, and inverse binary relations are considered. The presentation is supplied with a number of examples. In particular, the author interprets the notion of a graph as a binary relation. The notion of an equivalence relation and the construction of a quotient set are given in detail. The results obtained are used for introducing rational numbers and vectors.
The article is based on a lecture given by the author for secondary school teachers in the framework of the “International Soros Science Educational Program” and is aimed at presenting contemporary developments in mathematics on an elementary level understandable for secondary school teachers and pupils.