A way of showing students about the real numbers.
In the early stages of schooling, children are introduced to the number line. The first time they see this, it is populated only with the real, positive integers (1, 2, 3…).
Later on, the teacher and student can add the fractions, or more strictly, the real, positive, rational numbers.
Depending on the school, the next step is to realise that the number line extends backwards, past zero. This introduces the concept of negative numbers.
Bright students will, at this point, ask where the number line ends, and the teacher can use this question to introduce a first, limited notion of infinity.
Later on in the student’s career, they will be shown that some numbers cannot be expressed as rational fractions (one integer divided by another). These numbers, the surds, or irrational numbers, fill the remaining gaps in the number line.
Once the number line is filled, its usefulness as a teaching device is lessened, as the student should have a good grasp of all the numbers. The next, and possibly last time the line is used is as an introduction to imaginary and complex numbers, where the line forms the real part of the number (the horizontal axis of an Argand diagram).