In Nine Chapters on the Mathematical Art (Jiuzhang Suanshu), negative numbers were used in the chapter on solving systems of simultaneous equations. For instance, revenue numbers are considered positive, while expense numbers are deemed negative; or surplus amounts are viewed as positive, while deficit amounts are seen as negative. In a problem calculating grains, the increased grains are considered positive, and the lost grains, negative.

At the time, calculation was done by the method of suan chou (counting rods). Red rods were used to denote positive coefficients, and black ones to denote negative ones. Or in another case, the normal position of suan chou denoted positive, while an inclined position denoted negative.

Rules for the calculation of signed numbers were also given in Jiuzhang Suanshu.

According to the book, the deduction (or subtraction) of two numbers with the same sign (from another number) equals the deduction of the absolute values of the two numbers, while the deduction of two numbers with different signs equals the addition of the absolute values of the two numbers.

Also, a positive number subtracted from zero gives a negative number, whereas a negative number subtracted from zero gives a positive number. Inversely, zero plus a positive number is still a positive number, and zero plus a negative number is still a negative number.

The addition of two numbers with different signs equals the deduction of their absolute values, while the addition of two numbers with the same sign equals the addition of their absolute values.

Jiuzhang Suanshu gave the most complete depiction on the rules for adding and subtracting positive and negative numbers in the world until the 17th century.

In the thirteenth century, a diagonal stroke was drawn through the last nonzero digit of a number to mark it as a negative number.

Negative numbers appeared very late in the West. Many noted mathematicians did not admit negative numbers, because they consider zero as "nothing" and could not understand that something could be even less than "nothing," and so considered negative numbers "absurd." It was only in the 17th century when Descartes invented the coordinate system, which gave a geometrical explanation and an actual meaning for negative numbers, that negative numbers began to be accepted gradually.

The introduction of negative numbers is an important contribution of Chinese mathematicians to world mathematics. With the introduction of negative numbers, the whole numbers and rational numbers became complete.

Author: Jeff

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