Generalized associative and commutative laws

Milosav M. Marjanović

School algebra is not an abstract mathematical discipline but its variables denote the numbers from a number system which is under elaboration. Basic properties of a number system are in the same time basic rules of algebra. Which other rules have to be deduced is a matter of concern to those who research problems of teaching algebra in school. The commutative and associative laws are often seen formulated in math school books. But they have a full effect when they are used to define numerical value of sums and products of three and more members and when it is proved that this value is independent of the way how summands and factors are associated and ordered. To accept these proofs with understanding, students have to be prepared for deductive reasoning and to be acquainted with all different ways how elements of a set can be ordered and with the method of mathematical induction as well. Hence, it is a student of a serious secondary school of age 14 or more.