number line

A number line is a picture that turns numbers into places. Draw a straight horizontal line, mark a point as 0, and choose a unit length. Step right for positive numbers and left for negative ones. Now every number has a home, and you can literally see which numbers are bigger by looking at which lie farther right.

Formally, a number line is a line on which each point corresponds to exactly one real number, and each real number corresponds to exactly one point — a perfect one-to-one match. The point labeled 0 is the origin; equal steps mark off the integers, and the points in between hold all the fractions and irrationals.

The number line makes abstract ideas visual. Distance from 0 is absolute value; the order relation “less than” means “to the left of”; adding a positive number slides you right while adding a negative slides you left. Extending the line into a second, vertical direction gives the coordinate plane used in graphing.