12 Facts About Number line

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Alternatively, one real number line can be drawn horizontally to denote possible values of one real number, commonly called x, and another real number line can be drawn vertically to denote possible values of another real number, commonly called y Together these lines form what is known as a Cartesian coordinate system, and any point in the plane represents the value of a pair of real numbers.

Further, the Cartesian coordinate system can itself be extended by visualizing a third number line "coming out of the screen ", measuring a third variable called z Positive numbers are closer to the viewer's eyes than the screen is, while negative numbers are "behind the screen"; larger numbers are farther from the screen.

Real Number line carries a standard topology, which can be introduced in two different, equivalent ways.

Real Number line is trivially a topological manifold of dimension 1.

Real Number line is a locally compact space and a paracompact space, as well as second-countable and normal.

The real Number line is contractible, and as such all of its homotopy groups and reduced homology groups are zero.

Alternatively, the real Number line has two ends, and the resulting end compactification is the extended real Number line.

Real line is a vector space over the field of real numbers of dimension 1.

Real Number line carries a canonical measure, namely the Lebesgue measure.

Lebesgue measure on the real Number line is one of the simplest examples of a Haar measure on a locally compact group.