However, the developed brain's understanding of the objective world has reached a more rational and abstract level. 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, a wild animal is captured, which is represented by 1 stone. If you catch three heads, put three stones.
"Knotting knots" is also something that many close ancient humans have done. There is a record of "tying the knot to govern the country" in the book of changes.
Legend has it that the ancient Persian kings tied knots with ropes to count the days of war. It is also a common method used by the ancients to carve or hide the bark with sharp tools or count it on the ground with small sticks.
When these methods are used much more, the concept of number and the symbol of counting are gradually formed. At first, the concept of numbers began with natural numbers, such as 1, 2, 3, 4 ... No matter where they are located, the symbols used for counting 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).
No matter how the positions of these seven symbols change, the numbers they represent are the same. When they are combined according to the following rules, they can represent any number: 1 Number of repetitions: A Roman numeral symbol is repeated several times, indicating several times of this number.
For example, "three" means "3"; "XXX" means "30" 2. Add right and subtract left: add a symbol representing big numbers to the right of the symbol representing small numbers, indicating that big numbers are added with small numbers, such as "VI" for "6" and "DC" for "600".
A symbol representing a small number is attached to the left of the symbol representing a large number, indicating a number in which a large number is subtracted from a small number, such as "IV" for "4", "XL" for "40" and "VD" for "495". 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, notation was also very important. 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 chip used for calculation is made of bamboo sticks and bones.
Arranged according to the specified length order, which can be used for counting and calculation. With the popularization of calculation, the arrangement of calculation and preparation has become the symbol of calculation.
There are two types of calculation and arrangement, horizontal and vertical, both of which can represent the same number. It is clear from the absence of "10" in the calculation code that the calculation strictly follows the decimal system from the beginning.
Numbers exceeding 9 digits will 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. Because the decimal system was really used in other parts of the world at the end of the 6th century.
But there is no "zero" in digital calculation, and there is a vacancy when it meets "zero". For example, "6708" can be expressed as "┴ ╥". "
There is no "zero" in the number, so it 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 believe that the invention of the mathematical symbol "0" should be attributed to Indians in the 6th century. They first used a black dot () to represent zero, and then gradually became "0".
Speaking of the appearance of "zero", it should be pointed out that the word "zero" appeared very early in ancient Chinese characters. But at that time, it didn't mean "nothing", just "bits and pieces" and "not much".
Such as "odd", "sporadic" and "odd". "105" means that there is a score of 100.
With the introduction of Arabic numerals. "105" is pronounced as "105", and the word "zero" corresponds to "0", so "zero" means "0".
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 old-fashioned. He doesn't allow anyone to use "0".
A Roman scholar recorded some benefits and explanations about the usage of "0" in his notes, so he was summoned by the Pope and executed the punishment of "Zn" so that he could no longer hold a pen and write. But 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 germination of mathematics, there were many numerical decimal systems, such as five, binary, ternary, seven, eight, decimal, hexadecimal, twenty, hexadecimal and so on.
In the long-term practical application, decimal has finally gained the upper hand. 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 integrated ancient Greek mathematics into their own mathematics, and this simple and easy-to-remember decimal notation spread all over 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 human long-term practical activities. With the needs of production and life, people find that it is not enough to express it only by natural numbers.
If five people share four things when distributing prey, how much should each person get? So the score is generated. China's academic score is earlier than that of Europe 1400 years! Natural numbers, fractions and zeros are usually 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, advance and retreat, rise and fall, east and west.
To represent such a quantity, a negative number is generated. Positive integers, negative integers and zero are collectively called integers.
If you add a positive score and a negative score, 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.
2. The history and development history of numbers. Let's put everything related to numbers. The origin of numbers is the cornerstone of the building of mathematics, and it is also the earliest mathematical object studied by people.
Millions of years ago. Our ancestors only knew the concepts of "you", "nothing", "more" and "less", but they didn't know what numbers were.
With the progress of civilization, these vague concepts can no longer meet the needs of production and life. For example, in the ancient book Zhouyi, there is a record of "knotting the ancient".
That is, when an important event happens, tie a knot on the rope as a mark. Although this method is simple, it at least shows that people already have the concept of number.
After writing appeared, people tried to record mathematics in the form of symbols. So there are all kinds of recording methods.
The ancient Egyptians used "|" to indicate one and "∨" to indicate two; The ancient Romans used "I" for one and "II" for two. Although this method is effective, it is very inconvenient to record in a very large number of cases.
For example, if we want to express for one hundred hours, should we write one hundred "|"? Of course, the ancient Romans also saw the problem, so they invented Roman numerals I, II, III, IV, V, VI, VII, VIII, IX, X, L and C to stand for 1, 2, 3, 4, 5, 6, 7 and 8 respectively. It seems that the problem has been solved, but it is still difficult to express 10 thousand.
This is why Roman numerals are not widely used. The failure of Roman numerals shows that any counting method that wants each number to correspond to a symbol is futile.
Until the eighth century, Indians invented a notation that only contained 1, 2, 3, 4, 5, 6, 7, 8, 9 and 9 symbols, and agreed that the position of numbers determined the size of numbers. For example, in the number 89, 8 means eight tens and 9 means nine ones.
This means that any number is a piece of cake. As a result, this invention was quickly brought into the Arab capital Baghdad by businessmen.
And soon spread, called Arabic numerals. Because this notation is simple and clear, it has been used ever since.
Become the universal language of mathematics in the world. No wonder Engels called it "the most wonderful invention".
* * * * * * * * * * * * * * There are many ways for Arabic numerals to come from all countries in the world, and one of them is internationally accepted, that is, Arabic numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8. In fact, Arabic numerals were not invented by Arabs, but by ancient Indians.
Ancient Indians carved some horizontal lines on stone tablets to indicate numbers, one horizontal line indicated 1 and the other horizontal line indicated 2 ... Later, they used palm leaves or birch bark as writing materials and connected some strokes, for example, two horizontal lines of 2 were written as z, three horizontal lines of 3 were written as z, and so on. In the 8th century AD, an Indian mathematician named Kank came to Baghdad, the capital of Arabia, with digital books and astronomical charts.
At this time, China's papermaking had just been introduced into Arabia. As a result, his book was quickly translated into Arabic and spread in the Arabian Peninsula, and Arabic numerals also spread to all parts of Arabia.
With the commercial exchanges between the East and the West, these figures were introduced to Europe by Arab businessmen in the12nd century. Europeans love this convenient and applicable notation, and they think it is Arabic numerals, which has caused this historical misunderstanding.
Although people later knew the truth of the matter, they never corrected it because they were used to it. After Arabic numerals spread to European countries, their appearance gradually changed due to reproduction. After more than 65,438+0,000 years of continuous improvement, it was not until 65,438+0,480 that the writing of these numbers was similar to the current writing.
1522, Arabic numerals appeared in the book "The Englishman and Stowe", which was basically consistent with the current writing. Because Arabic numerals and their decimal notation have many advantages, they are gradually spread all over the world and used by all countries in the world.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * The origin of Arabic numerals, which were created by ancient Indians, spread to the Arab region around the 7th century. By the 3rd century A.D./KLOC-0, the Italian mathematician Fibonacci wrote Abacus, in which he introduced Arabic numerals in detail.
Later, these figures spread from the Arab region to Europe. Europeans only know that these numbers are imported from the Arab region, so they are called Arabic numbers. Later, these figures spread from Europe to all countries in the world.
Arabic numerals were introduced into China around 13 ~ 14 century. Because there was a number called "chip" in ancient China, which was easy to write, Arabic numerals were not popularized and used in China at that time.
At the beginning of this century, with the absorption and introduction of foreign mathematical achievements by China, Arabic numerals began to be used slowly in China, and only now have they been popularized and used in China for more than 100 years. Arabic numerals have now become the most commonly used numbers in people's study, life and communication.
* * * * * * * * * * * * * * * * * * * The origin of Roman numerals is a quantitative representation that is rarely used now. It came into being later than the numbers in China and Oracle Bone Inscriptions, and even later than the Egyptian single digit.
However, its appearance marks the progress of an ancient civilization. About 2500 years ago, the Romans were still in the early stage of cultural development, when they used their fingers as computing tools.
To represent 1, 2, 3 and 4 objects, extend 1, 2, 3 and 4 fingers respectively; It means that five objects stretch out a hand; It means that 10 object sticks out two hands. This habit has been used by human beings until today.
People often use such gestures to represent numbers in conversation. At that time, in order to record these numbers, the Romans drew I, II and III on sheepskin instead of the number of fingers. In order to represent a hand, it is written as a "V", which represents the open shape of thumb and forefinger; When expressing two hands, it is drawn as "ⅴ ⅴ", and later it is written as "ⅹ", with one hand up and the other hand down, which is the prototype of Roman numerals.
Later, in order to represent a larger number, the Romans used the symbol C to represent 100, which is the first letter of the Latin word "century", which means 100. The symbol m stands for 1000.
M is the first letter of the Latin word "mile", which means 1000. Take half of the letter c as the symbol l, which means 50.
500 is represented by the letter D. If you draw a horizontal line at the top of the number, it will expand.
3. The development history of digital computers In the 1980s, the standard for mainframes was a computer with an operation speed of 6.5438+0 million times per second, a word length of 32-64 bits and a main memory capacity of 0.5-8 megabytes. Mainframes are mostly general-purpose machines, mainly used in computer communication networks. The standard of a medium-sized computer is a computer with a computing speed of 65438+ 10,000 to 1 10,000 times per second, a word length of 32 bits and a main memory capacity of less than 1 megabyte. Mainly used for the management of small and medium-sized local computer communication networks. There is no strict boundary between minicomputers and microcomputers. Common PC series machines include PC, PC/XT, PC286, VAX, etc. The structure of single chip microcomputer is very different. The main functional components of the above-mentioned computer are connected together by wires in a separated form to form a complete computer system, while the single chip microcomputer integrates all functional components together to form a computer with only one integrated circuit.