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正负数的由来

据史料记载,早在两千多年前,中国就有了正负数的概念。

三国时期的学者刘徽在建立负数的概念上有重大贡献。刘徽首先给出了正负数的定义,他说:“今两算得失相反,要令正负以名之。”意思是说,在计算过程中遇到具有相反意义的量,要用正数和负数来区分它们。

刘徽第一次给出了区分正负数的方法。他说:“两算得失相反,要另正负以名之;正算赤,负算黑;否则以斜正为异”。意思是说,用红色的小棍摆出的数表示正数,用黑色的小棍摆出的数表示负数;也可以用斜摆的小棍表示负数,用正摆的小棍表示正数。

在我国古代著名的数学专著《九章算术》(成书于公元一世纪)中,最早提出了正负数加减法的法则:“正负数曰:同名相除,异名相益,正无入负之,负无入正之;其异名相除,同名相益,正无入正之,负无入负之”。

这里的“名”就是“号”,“除”就是“减”,“相益”、“相除”就是两数的绝对值“相加”、“相减”,“无”就是“零”。用现在的话说就是:“正负数的加减法则是:同符号两数相减,等于其绝对值相减,异号两数相减,等于其绝对值相加。零减正数得负数,零减负数得正数。异号两数相加,等于其绝对值相减,同号两数相加,等于其绝对值相加。零加正数等于正数,零加负数等于负数。

这段关于正负数的运算法则的叙述是正确的,与现在的法则完全一致。负数的引入是我国数学家杰出的贡献之一。用不同颜色的数表示正负数的习惯,一直保留到了现在。用红色表示负数,报纸上登载某国经济上出现赤字,表明支出大于收入,财政上亏了钱。负数是正数的相反数,在生活中,我们经常用正数和负数来表示意义相反的两个量。

According to historical records, China had a positive and negative concept as early as two thousand years ago.


Liu Hui, a scholar of the Three Kingdoms period, made a major contribution to the concept of establishing negative numbers. Liu Hui first gave the definition of positive and negative numbers. He said: "The opposite of the two calculations is to make the positive and negative names." This means that in the process of calculation, a quantity with the opposite meaning is encountered. Numbers and negative numbers distinguish them.


For the first time, Liu Hui gave a way to distinguish between positive and negative numbers. He said: "The opposite of the two calculations, the opposite is to be positive and negative by name; it is considered red, negative black; otherwise it is different from oblique." This means that the number with a small red stick indicates a positive number, and the number with a small black stick indicates a negative number. You can also use a small pendulum to indicate a negative number, and a small pen with a positive pendulum to indicate a positive number.


In the famous ancient Chinese monograph "Nine Chapters of Arithmetic" (written in the first century AD), the law of positive and negative addition and subtraction was first proposed: "positive and negative numbers": the same name is divided, the name is different, no In the negative, the negative is not positive; its synonyms are divided, the same name is the same, and there is no positive, no negative."


The "name" here is the "number", the "division" is the "minus", the "division" and the "division" are the absolute values of the two numbers "added", "subtracted", "none" is the "zero" . In the present words: "The law of addition and subtraction of positive and negative numbers is: subtracting the two numbers of the same symbol, equal to the subtraction of its absolute value, subtracting the two numbers of the opposite sign, equal to the sum of its absolute values. Zero minus positive numbers are negative The zero-negative negative number is positive. The two numbers of the opposite sign are added, which is equal to the subtraction of the absolute value, and the two numbers of the same number are added, which is equal to the sum of their absolute values. The zero plus positive number is equal to the positive number, and the zero plus negative number is equal to the negative number.


The narrative of the algorithm for positive and negative numbers is correct and is completely consistent with the current law. The introduction of negative numbers is one of the outstanding contributions of Chinese mathematicians. The habit of expressing positive and negative numbers with numbers of different colors has been retained until now. Negative numbers are indicated in red, and a newspaper’s economic deficit appears in a newspaper, indicating that expenditures are greater than income and financially. Negative numbers are the opposite of positive numbers. In life, we often use positive and negative numbers to represent the two opposite quantities.


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