function
① indicates that there is no ② occupation ③ boundary ④ starting point ⑤ freezing point ⑤ is an accurate value (for example, 5. 1 accurate to two decimal places is 5. 10). Remember, 0 is not a negative number, but a number between positive and negative numbers. 0 is 0, which means no. ..
history
0 is an extremely important number, and the discovery of 0 is called one of the great discoveries of mankind. In ancient China, 0 was called Jinyuan number (meaning extremely precious number). The data of 0 is said to have been invented by Indians in the 5th century. 1202, a businessman wrote an abacus book. In the east, mathematics is mainly based on operation (in the west, it was written in geometry at that time). "Nine numbers of Indians, plus the symbol 0 invented by Arabs, can write all the numbers ..." For some reasons, when the symbol 0 was first introduced to the West, it once caused confusion in the West. At that time, because the west believed that all numbers were positive numbers, the number 0 would make many formulas and logics untenable (such as dividing by 0), and it was even considered as the devil's number, so it was banned. It was not until about 15 and 16 that zero and negative numbers were gradually recognized by westerners, which led to the rapid development of western mathematics. Another history of 0: the discovery of 0 began in India. About after A.D., the symbol "0" has been used in the Vedas, the oldest document in India. At that time, 0 in India meant no (empty) position. Around the beginning of the 6th century, India began to use the notation of fate. At the beginning of the 7th century, the great Indian mathematician Graf Magpuda first explained that 0 of 0 is 0, and any number can be obtained by adding or subtracting 0. Unfortunately, he didn't mention the example of calculating with the symbol of life position. Some scholars believe that the concept of "0" was born and developed in India because of the philosophical thought of "absolutely nothing" in Indian Buddhism. In 733 AD, an Indian astronomer introduced this notation to Arabs during his visit to Baghdad, the capital of Iraq, because it was simple and easy to use, and soon replaced the previous Arabic numerals. This symbol was later introduced into western Europe.
story
About 1500 years ago, European mathematicians did not know how to use the number "0". At this time, a scholar in Rome found the symbol "0" from the counting method in India. He found that with "0", it was very convenient to do mathematical operations. He was very happy to introduce the "0" method used by Indians to everyone. It was soon known to the Pope. At that time, the power of the church was very great, far exceeding that of the emperor. The Pope was very angry. He rebuked that the sacred number was created by God, and there was no "0" monster in the number created by God. Anyone who wants to use it now is blasphemy! So he ordered the arrest and torture of the scholar. In this way, "0" was banned by the Pope's order. Finally, "0" is widely used in Europe, but Roman numerals are gradually eliminated. There is no "zero" at the beginning of the 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 "0", it should be pointed out that the word "0" 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", which 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 any use of "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).
Mathematical attribute
0 is neither positive nor negative, but a number between positive and negative. When a certain number x is greater than 0 (that is, X>0), it is called a positive number; On the other hand, when x is less than 0 (that is, x
0 is a problem of natural numbers.
Historically, there have been two regulations at home and abroad about whether 0 is a natural number: one stipulates that 0 is a natural number, and the other stipulates that 0 is not a natural number. Since the founding of the People's Republic of China, the textbooks of primary and secondary schools in China have always stipulated that the set of natural numbers does not include 0. At present, most foreign mathematicians stipulate that 0 is a natural number. In order to facilitate international exchanges, national standards stipulate that natural number set includes 0. Therefore, in our newly published textbooks, this treatment is carried out in accordance with national standards, and the original natural number set is now called positive integer set. At the same time, we also use some mathematical symbols according to the national standards. From the point of view of use, it doesn't matter much whether the set of natural numbers contains 0. As ordinal number, starting from 0 is the same as starting from 1; We used to say n∈N, now we just need to say that n is a positive integer.
Edit the factors and multiples of this paragraph.
When aхb=c( a, b and c are integers), define that a and b are factors of c, c is a multiple of b ∫aх0 = 0(a is an arbitrary real number) ∴a is a factor of 0, and 0 is a multiple of a, so 0 must be the least common multiple; The other a≥0, so a is the greatest common factor.
Divide by 0 problem
The reason why 0 can't divide (denominator and postterm) (1) The mathematical reason why 0 can't divide (denominator and postterm): * 1 If the divisor (denominator and postterm) is 0 and the dividend is a non-zero natural number, the quotient does not exist. This is because any number multiplied by 0 will not give a non-zero natural number. *2 If the divisor (denominator and last term) of the dividend is equal to 0, in this case, the quotient is not unique and can be any number. This is because any number multiplied by 0 is equal to 0. (2) Physical reason why 0 can't be divided: A positive integer x (dividend) divided by another positive integer n (divisor) means the size of each share after dividing the dividend into n equal parts. The physical meaning of dividing by 0 is to divide an object into 0 parts, that is, to completely eliminate an existing object and make it disappear into the universe. But in general physical and electrical calculations, 0 is generally considered to be infinitesimal. Einstein's theory of relativity reveals the relationship between matter and energy. This theory shows that matter and energy in the whole universe are conserved and it is impossible to completely destroy an object. Sometimes an object seems to disappear, but in fact it is transformed into energy. Dividing by 0 violates the law of conservation of mass and energy in the physical sense. 2. Suppose it is meaningful to infer the size of 1/0. If it is meaningful to divide by 0, how big is it? If 1 is divided by a smaller and smaller positive number, you get a larger and larger positive number. 1/0. 1 = 10 1/0.0 1 = 100 1/0.00 1 = 1000 ...0y & gt； When n approaches 0, y becomes larger and larger. Similarly, if 1 is divided by an increasing negative number, you get an decreasing negative number. 1/-0. 1 =- 10 1/-0.0 1 =- 100 1/-0.00 1 =- 1000.0y & lt； 0 As n approaches 0, y becomes smaller and smaller. But when n=0, y is not equal to positive infinity or negative infinity (derived from positive and negative angles). 1/0 is greater than infinity, 1/0 is less than infinitesimal, and 1/0 is a limit number. This limit number 1/0 is both maximum and minimum, but the maximum number in all real numbers is also minimum, and the maximum and minimum are unified in 1/0.
x=0
x？ =0 x？ =0 x？ =0 nx=0 xf(x)=0 0*∞ meaningless 0-n meaningless
In computer science, 0 is usually used to represent "false" Boolean values. The database of the computer consists of binary, namely 0 and 1. When the circuit transmits data, 0 and 1 represent low potential and high potential respectively. The on-off of the switch indicates 0 and 1. In programming languages, if the number of arrays is 4, then its actual members are 0 to 3, not 1 to 4. In C language, 0 is put before integer constant to represent octal number, while integer hexadecimal number usually starts with 0x. The existence of 0 must not be ignored, otherwise you will hit a wall everywhere in the programming world! In the space console, there is only "0" console, and there is no "1" console! In chemistry, zero valence means simple substance, and group 0 means rare gas.
Edit this paragraph in American culture.
In American culture, 0 means a little pain. This also represents the end. 0 is the inserter and the passive in GAY. Call it receiving. 0.5 is both offensive and defensive. 1 play an active role. Call it an attack.
Edit this paragraph in human culture.
In the 6th century, because the Roman Empire converted to Christianity after Constantine the Great, monks decided to change the year of Jesus' birth to 1. But at present, whether there is 0 years is still controversial.