Number line

For other uses, see Number line (disambiguation).

This article covers basic topics. For advanced topics, see Real line.

In basic mathematics, a number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point. Often the integers are shown as specially-marked points evenly spaced on the line. Although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing forever in each direction, and also numbers not marked that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers.

It is divided into two symmetric halves by the origin, i.e. the number zero.

In advanced mathematics, the expressions real number line, or real line are typically used to indicate the above-mentioned concept that every point on a straight line corresponds to a single real number, and vice versa.

Drawing the number line

The number line is usually represented as being horizontal. Customarily, positive numbers lie on the right side of zero, and negative numbers lie on the left side of zero. An arrowhead on either end of the drawing is meant to suggest that the line continues indefinitely in the positive and negative real numbers, denoted by $\mathbb{R}$. The real numbers consist of irrational numbers and rational numbers, as well as the integers, whole numbers, and the natural numbers (the counting numbers).

A line drawn through the origin at right angles to the real number line can be used to represent the imaginary numbers. This line, called imaginary line, extends the number line to a complex number plane, with points representing complex numbers. Children, mostly from 3rd grade to 5th grade, start to learn the basics of a number line. Number lines are also on rulers.

See also

• Coordinate system
• Complex plane
• Extended real number line
• Number form (neurological phenomenon)
• Line (geometry)
• Real number
• Timeline