Numerical ray

Numerical ray

A numeric ray is a graphical representation of non-negative numbers in the form of a ray . On the ray, as a rule, natural numbers are marked. The distance between adjacent points is equal to the unit of measurement ( unit interval ), which is set arbitrarily. The beginning of the ray is assigned the number 0. The ray is usually oriented to the right. The numerical ray is part of the numerical axis ^{[1] [2]} .

A numerical ray plays a large role in illustrating the concept of “ natural series of numbers”, allows you to compare natural numbers , focusing on their location on a numerical ray, allows you to perform counting and counting in parts based on a numerical ray ^{[3] [4]} . Another role of the numerical ray is that, using this concept, it is possible to introduce children to a rectangular coordinate system (numerical or coordinate angle), negative numbers ( numerical line ).

Adding the division operation to the concept of natural numbers leads to the appearance of a set of rational numbers , which can also be displayed on a number ray, where it will be located densely , but they do not occupy the entire ray. It can be proved, for example, using the Pythagorean theorem ^[5] that among the rational numbers among the rational numbers there are gaps - real numbers . It is possible, using the principle of Weierstrass intervals embedded on a number ray, to uniquely determine each real number. In this case, intervals with ends at the points representing rational numbers on the number ray are taken for the intervals. The Weierstrass method is based on the geometric constructions of the ancient Greek mathematician Eudoxus of Cnidus ^[6] .