 With the full set of integers, we can now construct the number line in order to use numbers to measure distances. We need to associate each number to a point on a line. To construct a correspondence between positive integers and points on a line, we begin by marking off equal segments to the right of the origin, p, of a given line. We associate the number one with the rightmost endpoint of the first segment, two with the rightmost endpoint of the second segment, etc. This method associates each positive integer with a point on the line. The number associated with a point is called its coordinate. We then associate the number zero with the origin and then extend the line to the left in the same sized segments we counted off on the right. These points correspond to the negative numbers where the leftmost point in the first segment represents minus one, the leftmost point in the second segment represents minus two, and so forth. This is the basic number line for the set of all integers. In order to indicate that these numbers are carried out to the right and to the left without limit, we introduce the symbols plus infinity and minus infinity. But we need to keep in mind that these are not numbers.