The number line is a straight line, extending indefinitely in both directions, on which every point represents a real number and every real number is represented by a point. Formally, it is an injective map from the real numbers to a line in Euclidean space. Below is an example of part of the number line, only showing the area between 9 and -9.
The number line's primary use is pedagogy, to help visualize operations on the reals. Addition is translation, and multiplication is scaling about the origin. The number line sees little use on its own in higher mathematics, but its concept can be extended into far more useful concepts such as the complex plane and function graphing.