Humans are the product of animal evolution, and there was no concept of quantity at first. The developed human brain has reached a more rational and abstract understanding of the objective world. In this way, in the long life practice, out of the need to record and distribute daily necessities, the concept of number has gradually emerged. For example, capture a wild animal, represented by 1 stone, and capture three heads. Just put three stones. "Knots" were also made by many very close ancients on earth. There is a record of "tying a rope to rule" in China's ancient book The Book of Changes. It is said that the ancient Persian kings tied a rope to count the days during the war. It is also a common method used by the ancients to carve bark or hides with sharp tools or count them on the ground with sticks. These methods are being used more and more.

At first, the concept of numbers began with natural numbers such as 1, 2, 3 and 4. , but the symbols of the numbers are the same size.

The figures in ancient Rome were quite advanced, and now many old wall clocks are often used.

In fact, Roman numerals have only seven symbols: I (for 1), V (for 5), X (for 10), L (for 50), C (for 100), D (for 500) and M (for 65438).

1. Repetition: A Roman numeral symbol is repeated several times, indicating several times of this number. For example, "three" means "3"; "XXX" means "30"

2. Right plus left minus: symbols representing big numbers, and symbols representing small numbers on the right, indicating big numbers plus small numbers, such as "VI" for "6" and "DC" for "600". On the left of the symbol representing big numbers, there is a symbol representing small numbers to indicate the number of big numbers minus small numbers, for example, "IV" stands for "4", "

3. add a horizontal line: add a horizontal line to the Roman numeral, indicating that it is 1000 times that number. For example, ""means "15000" and "165000".

In ancient China, we also attached great importance to notation. The oldest notation is found in Oracle Bone Inscriptions and Zhong Ding, but it is difficult to write and identify, so it is not used by future generations. In the Spring and Autumn Period and the Warring States Period, production developed rapidly. In order to meet this need, our ancestors created a very important calculation method-calculation. The computing chips used in the calculation are bamboo sticks and bones. If they are arranged in the specified order, they can be used for counting and operation.

From the fact that there is no "10" in the notation, it can be clearly seen that the notation strictly follows the decimal system from the beginning. Numbers exceeding 9 digits must enter one digit. The same number, a hundred in a hundred, Wan Li has ten thousand. This calculation method was very advanced at that time. Decimal system did not exist in notation because it was really used in other parts of the world at the end of the 6th century. "When it comes to' zero', it is empty. For example, "6708" can be expressed as "┴ ╥". There is no "zero" in the number, which is easy to make mistakes. So later, some people put copper coins in the blank to avoid mistakes, which may be related to the emergence of "zero" However, most people think that the invention of the mathematical symbol "0" should be

Speaking of the appearance of "0", it should be pointed out that the word "0" appeared very early in ancient Chinese characters. However, at that time, it didn't mean "nothing", only "bits and pieces" and "not much". Such as "odd", "odd" and "odd". "105" means: 100 miles away.

If you look closely, you will find that there is no "0" in Roman numerals. In fact, in the 5th century, "0" was introduced to Rome. But the Pope is cruel and conservative. He doesn't allow any use of "0". A Roman scholar recorded some benefits and explanations about the use of "0" in his notes, so he was summoned by the Pope and executed the penalty of "z m ℉ n".

However, no one can stop the appearance of "0". Now, "0" has become the most meaningful digital symbol. "0" can mean "No" or "Yes". For example, a temperature of 0℃ does not mean that there is no temperature; "0" is the only neutral number between positive and negative numbers; The power of 0 of any number (except 0) is equal to1; 0! = 1 (factorial of zero is equal to 1).

In addition to decimal system, in the early stage of the budding of mathematics, there were many numerical decimal systems, such as five, binary, ternary, seven, eight, decimal, hexadecimal, twenty, sexagesimal and so on. In the long-term practical application, the decimal system finally prevailed.

At present, the internationally used numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 are called Arabic numerals. In fact, they were first used by ancient Indians. Later, Arabs incorporated ancient Greek mathematics into their own mathematics, and spread this simple and easy-to-remember decimal notation throughout Europe, gradually evolving into today's Arabic numerals.

The concept of numbers, the writing of numbers and the formation of decimal system are all the results of long-term human practice.

With the needs of production and life, people find that it is not enough to express only natural numbers. If five people share four things when distributing prey, how much should each person get? So the music score was produced. China's research on music score is earlier than Europe's 1400 years! Natural numbers, fractions and zeros are generally called arithmetic numbers. Natural numbers are also called positive integers.

With the development of society, people find that many quantities have opposite meanings, such as increase and decrease, forward and backward, up and down, east and west. In order to express such quantities, negative numbers, positive integers, negative integers and zero are collectively called integers. If the positive and negative fractions are added together, they are collectively called rational numbers. With these digital representations, people find it much more convenient to calculate.

However, in the process of digital development, an unpleasant thing happened. Let's go back to Greece 2500 years ago, where there was a Pythagorean school, a group that studied mathematics, science and philosophy. They believe that "number" is the source of all things and dominates the whole nature and human society. Therefore, everything in the world can be summed up in a number or the proportion of numbers. This is the source of beauty and harmony in the world. By numbers, they mean integers. The appearance of scores makes "number" less complete. But all the scores can be written as the ratio of two integers, so their faith has not wavered. However, when a student named hippasus studied the term in the ratio of 1 2, he found that no number could represent it. If this number is x, because the result of deduction is x2=2. He drew a square with a side length of 1 and set the diagonal as X. According to Pythagorean theorem x2= 12+ 12=2, it can be seen that the diagonal length of a square with a side length of 1 is the number he is looking for, and this number must exist. But what is this? How to express it? Hippasus and others were puzzled and finally decided that this was a new number that they had never seen before. The appearance of this new number shocked the Pythagorean school and shook the core of their philosophical thought. In order to keep the math building that supports the world from collapsing, they stipulated that the discovery of new numbers should be kept secret. But hippasus couldn't help letting the cat out of the bag. It is said that he was later thrown into the sea to feed sharks. However, the truth cannot be hidden. People later discovered many numbers that could not be written by the ratio of two integers, such as pi. People write them in π and other forms and call them irrational numbers.

Rational numbers and irrational numbers are collectively called real numbers. The study of various numbers in the range of real numbers makes the mathematical theory quite profound and rich. At this time, human history has entered the19th century. Many people think that the achievement of mathematics has reached its peak, and there will be no new discoveries in digital form. But when solving the equation, you often need to make a square. If the square is negative, is there any solution to this problem? If there is no solution, mathematical operation is like walking into a dead end. So mathematicians stipulated that the symbol "I" was used to represent the square root of "-1", that is, I =, and the imaginary number was born. "I" became an imaginary unit. Later generations combined real numbers with imaginary numbers and wrote them in the form of A+BI (A and B are both real numbers). This is because people can't find quantities expressed by imaginary numbers and complex numbers in real life, so imaginary numbers always make people feel illusory. With the development of science, imaginary numbers have been widely used in hydraulics, cartography and aviation. In the eyes of scientists who master and use imaginary numbers, imaginary numbers are not "virtual" at all.

After the concept of number developed to imaginary number and complex number, for a long time, even some mathematicians thought that the concept of number was perfect, and all the members of the mathematical family had arrived. However, in June 1843+16 10, British mathematician Hamilton put forward the concept of "quaternion". The so-called quaternion is a kind of shape number. It consists of a scalar (real number) and a vector (where x, y and z are real numbers). Quaternions are widely used in number theory, group theory, quantum theory and relativity. At the same time, people have also studied the theory of "multivariate number". Multivariate number has gone beyond the category of complex number, and people call it hypercomplex number.

Due to the development of science and technology, concepts such as vector, tensor, matrix, group, ring and domain are constantly emerging, which pushes mathematical research to a new peak. These concepts should also belong to the category of numerical calculation, but it is not appropriate to classify them into super complex numbers. Therefore, people call complex numbers and hypercomplex numbers narrow numbers, while concepts such as vector, tensor and moment A are called generalized numbers. Although there are still some differences in the classification of numbers, the concept of numbers is still recognized.