For example, if there is not a peach on the plate, it can be said that there are 0 peaches on the plate. 0 can indicate the starting point, for example, the meaning indicated by the leftmost scale 0 in a ruler is the starting point of measurement. The length from 0 to 1 on the scale is exactly 1 cm.

2. Although 0 means "no" in quantity, it still has the same treatment as other numbers, that is, it can "participate in the operation" with other numbers (0 cannot be divided completely) to solve the problem. For example, the result of subtracting the same two numbers is 0; The sum of a number and 0 is itself; The difference between a number MINUS 0 is itself; The quotient of 0 divided by any number that is not 0 is 0; The product of 0 times any number is 0.

3,0 can be used as a placeholder.

In the decimal counting rule, it is stipulated that "there is no one in the middle or at the end, just write 0 on that bit", and 0 plays a "placeholder" role at this time.

4. "0" can represent a "definite quantity"

"0" means that there is a certain quantity in certain places. For example, "0 o'clock" does not mean that there is no time, but refers to a specific time, namely 12 or 24 o'clock in the middle of the night. Similarly, "0℃ is not without temperature, but" the temperature at which fresh water begins to freeze ".

5. "0" is a number without state.

When counting, 0 acts as a placeholder and cannot be omitted. However, the "0" after the decimal point shows the state of "dispensable". Add or delete 0 at the end of the decimal, and the size of the decimal remains the same.

For example, 0.70 and 0.7 are two equal decimals, and 0 in the percentile is "dispensable". Similarly, when learning "fractional division", if the number of digits in the dividend is not enough, you can add 0 to the end of the dividend to continue the division. Of course, if the dividend is an integer, you need to add 0 after the decimal point.

6. "0" is a number that cannot be ignored.

In "Properties of Decimals", 0 means "distributability": add or remove 0 at the end of decimals, and the size of decimals remains unchanged. However, when representing the approximate value of the decimal, the 0 at the end of the decimal cannot be omitted. For example, 0.984 with a decimal place (accurate to ten digits) is 1.0, and the 0 at the end of 1.0 cannot be removed.

7. "0" can mean "origin"

In Cartesian coordinate system, 0 is the origin of this spatial coordinate system. The straight line defining the origin, positive direction and unit length is the number axis, the number represented by the origin is 0, and 0 is the dividing point of positive and negative numbers.

Extended data

The standard number 0 was invented by ancient Indians around the 5th century. They first used a black dot to represent zero, and then gradually became "0". In eastern countries, mathematics is mainly based on operation (in the west, geometry was written at the beginning, "nine numbers of Indians, plus the 0 symbol invented by Arabs, can write all the numbers).

For some reason, when the symbol 0 was first introduced to the west, it caused confusion in the west, because at that time, the west thought that all numbers were positive numbers, and the number 0 would make many formulas and logics untenable (such as dividing by 0), and even thought it was a devil's number, so it was forbidden to use it. 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. Around 2000 BC, the symbol "0" was used in Vedas, the oldest Brahmin literature in ancient India. At that time, 0 indicated that there was no (empty) position in Brahmanism in India.

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.

Baidu Encyclopedia -0