Two numbers can be added by "picking up" the length from 0 to one of the numbers, and putting it down again with the end that was 0 placed on top of the other number. Thus, for example, the length of a line segment between 0 and some other number represents the magnitude of the latter number. Taking this difference is the process of subtraction. The distance between them is the magnitude of their difference-that is, it measures the first number minus the second one, or equivalently the absolute value of the second number minus the first one. If a particular number is farther to the right on the number line than is another number, then the first number is greater than the second (equivalently, the second is less than the first). The line continues indefinitely in the positive and negative directions according to the rules of geometry which define a line without endpoints as an infinite line, a line with one endpoint as a ray, and a line with two endpoints as a line segment. Another convention uses only one arrowhead which indicates the direction in which numbers grow. According to one convention, positive numbers always lie on the right side of zero, negative numbers always lie on the left side of zero, and arrowheads on both ends of the line are meant to suggest that the line continues indefinitely in the positive and negative directions.
Drawing the number line Ī number line is usually represented as being horizontal, but in a Cartesian coordinate plane the vertical axis (y-axis) is also a number line. In particular, Descartes's work does not contain specific numbers mapped onto lines, only abstract quantities. Ĭontrary to popular belief, Rene Descartes's original La Géométrie does not feature a number line, defined as we use it today, though it does use a coordinate system. In his treatise, Wallis describes addition and subtraction on a number line in terms of moving forward and backward, under the metaphor of a person walking.Īn earlier depiction without mention to operations, though, is found in John Napier's A description of the admirable table of logarithmes, which shows values 1 through 12 lined up from left to right. The first mention of the number line used for operation purposes is found in John Wallis's Treatise of algebra.