Where do negative numbers come from? What is the history of negative numbers?

Negative numbers had already sprouted in the Western Han Dynasty in China, and first appeared as the object of mathematical research in the Nine Chapters of Arithmetic in the first century AD.

Just give an example.

Total Profit = Sum of Profits.

However, it is possible to lose money.

This loss is expressed as a negative number in the profit column.

When calculating the total profit, the whole is still summed.

Such a positive + negative number operation is convenient in some ways.

The history of negative numbers is:

As early as more than 2,000 years ago, China had the concept of positive and negative numbers and mastered the algorithm of positive and negative numbers. When people calculate, they use some small bamboo sticks to lay out various numbers to calculate.

Liu Hui, a scholar of the Three Kingdoms period in China.

Significant contribution to the establishment of the concept of negative numbers. Liu Hui first gave the definition of positive and negative numbers, he said: the two are opposite to the gains and losses, and the positive and negative should be named. This means that when you encounter quantities with opposite meanings during the calculation, you should distinguish them by positive and negative numbers.

For the first time, Liu Hui gave a method for distinguishing positive and negative numbers. He said, "Positive is red, negative is black; Otherwise, it is different from oblique positive.

This means that a number posed with a red stick represents a positive number, and a number posed with a black stick represents a negative number; It is also possible to use a small stick with an oblique swing to represent a negative number, and a small stick with a positive swing to represent a positive number.

Calculation of negative numbers:

Addition: Negative number 1 + negative number of leakage groups 2 = - (negative number 1 + negative number 2) = negative number.

Negative number + positive number = sign takes the absolute value.

The sign of the larger additive number, the value is taken as the value obtained by subtracting the smaller absolute value from the larger absolute value.

Subtraction: Negative 1 Negative 2 = Negative 1 + (Positive 2) = Negative 1 plus the opposite of Negative 2.

Then calculate it according to the method of adding negative numbers to positive numbers.

Negative number Positive number = (positive number + negative number) = negative number The two numbers of different numbers are equal to the addition of their absolute values.

Multiplication: Negative 1 Negative 2 = (Negative 1 Negative 2) = Positive.

Negative Positive = (Positive Negative) = Negative.

Division: Negative 1 Negative 2 = (Negative 1 Negative 2) = Positive.

Negative Positive = (Negative Positive) = Negative.

In general, the division of the same sign equals a positive number, and the division of a different sign equals a negative number.

China was the first country in the world to recognize and apply negative numbers, and as early as the 4th century BC, Chinese mathematicians already understood the concepts of negative numbers and zeros in the "Nine Chapters of Arithmetic". The "Nine Chapters of Arithmetic" in the first century A.D. said, "Positive and negative arithmetic says: the same name is divided, different names are beneficial, positive and negative are not negative, and negative is not positive."

Its different names are divided by each other, the same name is beneficial, the positive is not into the positive, and the negative is not into the negative. ”

It is to the effect of "subtraction: when encountering numbers with the same symbol, they should subtract their values, and when encountering numbers with different symbols, they should add their values, the difference between zero and positive numbers is negative, and the difference between zero and negative numbers is positive." The "non-entry" in the above text is often considered by historians of mathematics to be the concept of zero.

The role of negative numbers:

1. Negative numbers are the occurrence of scrambling under the premise of artificially stipulating the direction of positive and vertical search.

2. Negative numbers are often used to indicate quantities that have the opposite meaning of positive numbers.

3. When choosing whether to use positive or negative numbers, first look at whether the positive direction is specified.

4. Generally, the quantity containing positive meaning is expressed as a positive number, and the quantity containing a derogatory meaning is expressed as a negative number.

For example, 5° above zero is represented by +5; -5° is denoted by -5. Income of 2000 yuan is expressed as +2000 yuan; The expenditure of 500 yuan is expressed as -500 yuan.

Negative numbers are a mathematical term, numbers smaller than 0 are called negative numbers, and negative numbers and positive numbers represent quantities with opposite meanings.

Any positive number preceded by a negative sign becomes a negative number. A negative number is the opposite of its absolute value. On the number axis, negative numbers are on the left side of 0, and the earliest record of negative numbers is the ancient mathematical work "Nine Chapters of Arithmetic" in China.

It is specified in the calculation"Positive is red, negative is black", that is, the red arithmetic chip is used to represent a positive number, and the black number is a negative number. The two negative numbers are compared to the size, and the absolute value is larger than the smaller.

Applications

Negative numbers can be widely used in temperature, floors, altitude, water level, profitability, increase or decrease in production, expenditure, income, score, deduction points, and so on. He is currently in the sixth grade of primary school. (There are also schools in the first year of junior high school).

A negative number is a number smaller than zero, the negative number is on the left side of the number axis, and zero is the dividing line between positive and negative numbers. Negative numbers are commonly used in front of them"-"number. Negative numbers are divided into negative integers and negative fractions. Negative numbers are made up of rational and irrational numbers, such as: - 2

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Liu Hui, a scholar of the Three Kingdoms period of China, made significant contributions to the establishment of the concept of negative numbers. Liu Hui first gave the definition of positive and negative numbers: "The gains and losses of the two calculations are opposite to Zheng Shu, and the positive and negative should be named after them", that is, when encountering quantities with opposite meanings in the calculation process, positive and negative numbers should be used to distinguish them.

For the first time, Liu Hui gave a method to distinguish between positive and negative numbers: "Positive is red, negative is black; Otherwise, it is different from oblique positive", that is, the number posed with a red stick represents a positive number, and the number posed with a black stick represents a negative number; It is also possible to use a small stick with an oblique swing to represent a negative number, and a small stick with a positive swing to represent a positive number.

In the famous ancient Chinese mathematical treatise "Nine Sides of the Chapters of Arithmetic", the law of addition and subtraction of positive and negative numbers was first proposed: "Positive and negative numbers are said: the same name is divided, different names are beneficial, positive and negative are not negative, and negative is not positive; Its different names are divided, the same name is beneficial, positive and non-positive, negative is not negative", that is, the law of addition and subtraction of positive and negative numbers is the same sign of two numbers or subtraction, which is equal to the subtraction of its absolute value, and the subtraction of two numbers of different signs is equal to the addition of its absolute value.

Zero minus positive numbers gives negative numbers, and zero minus negative numbers get positive numbers. The addition of two numbers with different signs is equal to the subtraction of their absolute values, and the addition of two numbers with the same sign is equal to the addition of their absolute values. Zero plus a positive number equals a positive number, and a zero plus negative number equals a negative number.

This involves the history of mathematics and cannot be abbreviated.

Liu Hui, a scholar during the Three Kingdoms period in China, made significant contributions to the establishment of the concept of negative numbers.

Liu Hui first gave the definition of positive and negative numbers, he said: "Today's two are opposite to each other, to."

Make the positive and negative in the name. "Meaning, encountering locust spikes during the calculation has the opposite meaning.

to distinguish them from positive and negative numbers.

For the first time, Liu Hui gave a method for distinguishing positive and negative numbers. He said, "Yes."

Red, negative is black; Otherwise, it is different from the evil and the good"Meaning, with a small red stick.

The number represents a positive number, and the number posed with a small black stick represents a negative number; It is also possible to use a diagonal pendulum.

The small stick represents a negative number, and the small stick with a positive swing indicates a positive number.

The famous mathematical treatise "Nine Chapters of Arithmetic" in ancient China (written in the first A.D.

In the period, the law of addition and subtraction of positive and negative numbers was first proposed: "Positive and negative numbers are said: the same name."

In addition, the name of the different lead is beneficial, the positive is not negative, and the negative is not positive; Its different names are divided into the same name.

Mutual benefit, positive does not enter the positive, negative does not enter the negative. ""Name" here"That's it."", "Except.""Only.

It's "minus."", "Mutually beneficial."", "Divide.""It is the absolute value of the two numbers."", "Subtract."""None.""

It's "zero."".

In today's parlance: "The law of addition and subtraction of positive and negative numbers is: two numbers with the same symbol."

Subtraction is equal to the subtraction of its absolute value, and subtraction of two numbers of different signs is equal to the addition of its absolute value.

Zero minus positive numbers gives negative numbers, and zero minus negative numbers get positive numbers. The sum of the two numbers equals its absolute.

The values are subtracted, and the two numbers of the same sign are added together, which is equal to the addition of their absolute values. Zero plus a positive number equals positive.

number, zero plus negative number equals negative number. "

This narrative of the algorithm of positive and negative numbers is entirely correct, and is in keeping with the current spinal movement.

The laws are exactly the same! The introduction of negative numbers is one of the outstanding contributions of mathematicians in China.

The habit of using numbers of different colors to represent positive and negative numbers has been retained until now.

Nowadays, red is generally used to indicate negative numbers, and newspapers publish a table of a country's economic deficit.

Ming's expenditure is greater than its income, and it loses money financially.

A negative number is the opposite of a positive number. In real life, we often use positive numbers.

and negative numbers to represent two quantities of opposite significance. In the summer, the temperature in Wuhan is as high as 42°C, and you will.

Thinking of Wuhan is indeed like a furnace, the temperature in Harbin in winter is -32 °C, a negative sign makes you feel.

The cold of the northern winter

More than 1,700 years ago, Chinese mathematician Liu Hui first clearly put forward the concept of positive and negative numbers. He also stipulates that when calculating, "positive is red, negative is black", that is, red acid type is used to denote positive numbers, and black chips are used to indicate negative numbers. This record is seven or eight hundred years earlier than that of foreign countries.

At the same time, it also stipulates the rules of addition and subtraction of rational numbers, and believes that "positive and negative techniques say: the same name is beneficial, and the different name is divided." The "same name" and "different name" are the current "same name", "different name", "except" and "benefit" are "subtraction" and "addition", these ideas did not appear in the West until a hundred years later than China.

Negative numbers were not adopted until the 7th century in India, and in 628 CE, in the Indian book The Revised System of Brahma, negative numbers were interpreted as liabilities and losses.

In 1544, Steffey of Germany defined a negative number as a number that is smaller than any number in the hood of a hole. In 1545, the Italian card became the first European work on negative numbers.

More than 400 years ago, the French mathematician Girard used "+" for the first time to represent positive numbers, and "- to represent negative numbers.

In 1637, the French mathematician Descartes invented analytic geometry and established coordinates to correspond plane points to real numbers formed by negative, zero, and positive arrays, so that negative numbers were explained, thus accelerating people's recognition of negative numbers. However, it was not until the 19th century, when German mathematicians such as Weierstrass and others laid the logical foundation for integers, that negative numbers gained a consolidated position in modern mathematics.

In order to represent two quantities in opposite senses (e.g., profit loss, income and expenditure, ......It's not enough to just learn.

Therefore, there is a negative number, with a positive profit and a negative loss; Positive income and negative expenditure.

Negative number. Numbers less than 0 are called negative numbers (excluding 0), and numbers to the left of 0 on the number line are called negative numbers.

If a number is less than 0, it is said to be a negative number.

There are an infinite number of negative numbers, among which there are (negative integers, negative fractions, and negative decimals).