The real number line is divided by zero into two sets, the positive numbers (those that are greater than zero) and the negative numbers (those that are less than zero). This is a modern concept, however. From the time of Thales in 600 B.C., numbers had been accepted as a collection or system of units used to correspond to actual physical quantities. The Babylonians used arithmetic to express lengths and weights, to exchange money and merchandise, to calculate taxes, and to apportion shares of a harvest. By the time of the Greeks, the basis of mathematics was geometry and mathematicians explained and justified algebraic results by working with geometric arguments. In all these situations, only positive numbers were needed.

Sometime after A.D. 200, the Hindus introduced negative numbers to represent debts while using positive numbers to represent assets. The first known mention...