II. The First Extension of the Notion of Number

Abstract

With the last section we leave operations with integers, and shall treat, in a new chapter, the extension of the number concept. In the schools it is customary, in this field, to take in order the following steps:

1. Introduction of fractions and operations with fractions.

2. Treatment of negative numbers, in connection with the beginnings of operations with letters.

3. More or less complete presentation of the notion of irrational numbers by examples that arise upon different occasions, which leads, then, gradually, to the representation of the continuum of real numbers.

It is a matter of indifference in which order we take up the first two points. Let us discuss negative numbers before fractions.