Mathematical knowledge 0 is 1. The origin of mathematical knowledge.

There is a germ of 0 in Babylonian literature.

However, unlike now, the symbol of 0 is represented by spaces. For example, in order to represent 10 1, Babylon wrote 1 1. Secondly, in ancient Indian mathematics, the earliest record of 0 was found in 876 AD, and many mathematicians in Europe also agreed with this view.

In the 6th century, Indians began to use "…", which later became a circle. In the ninth century, it was fixed as today's "0".

The third 0' s hometown is in China. There is a record of 0 in the book of songs, the earliest poetry collection in China, but at that time, 0 meant "small raindrop at the end of the storm"

In China's ancient knot notation, 0 appeared in the negation of "yes", indicating "no". During the Wei and Jin Dynasties, Liu Hui, a famous mathematician from many countries, explained 0 very clearly when commenting on Nine Chapters of Arithmetic.

In the ancient almanac of China, the words "beginning" and "beginning" were used to mean "coffee". The neutral position of the abacus means "coffee".

Missing words in ancient books are indicated by □, and when "0" is recorded in mathematics, it is also indicated by □. On the one hand, in order to distinguish the two.

More importantly, it was written by China's ancient substitute brush. Writing "0" with a brush is much more convenient than writing "□", so 0 gradually becomes drawing "0" counterclockwise.

In ancient China, 0 was called Jinhe, which means precious.

2. What is the meaning of 0 in mathematics?

In primary school mathematics textbooks, the nature of "0" is scattered in various parts. Now it is summarized as follows: (1) 0 is a number and an integer. (2) In decimal notation, 0 is a placeholder. (3)0 is even. (4)0 is a multiple of any integer. (5) When any number is added to 0, its value remains unchanged, that is, a+0=0+a=a (6) If any number is subtracted from 0, its value remains unchanged, that is, A-0 = a*0=0*a=0 (9)0 divided by a non-zero number, and the quotient is equal to 0, that is, if A ≠. For example, 3 ÷ 0,0 ÷ 0, there is no such formula. After introducing the concept of absolute value, the absolute value of 0 is equal to 0, that is | 0 | = 0; After introducing the concept of exponent, the power of 0 of any non-zero number is equal to 1, that is, if a≠0, then a =1; Wait a minute. What you said should mean in advanced mathematics. In advanced mathematics, 0/0 refers to a limit type, not a ratio relationship. The solution of this limit is to use Robida's law, and the denominator of the molecule takes the derivative directly, so the limit is-1.

Answer supplement

There is a problem of -0, but there is a saying that the limit tends to zero from the left. Elementary mathematics is different from advanced mathematics. Don't always look at the problem of high numbers from the perspective of elementary mathematics.

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0 is an extremely important number, and the discovery of 0 is called one of the great discoveries of mankind. 0 was called Jinyuan number in ancient China, which means 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 mainly based on geometry and logic at that time). Because of the need of operation, the number 0 was naturally introduced. In China, the number 0 has been recorded for a long time.

1208, India's * * * numbers were introduced into this book, and it was written at the beginning that "the nine numbers of Indians, together with the 0 symbol invented by * * * people, can write all the numbers ..." For some reasons, when the symbol 0 was first introduced to the West, it once caused confusion for Westerners, because at that time, the West thought that all the numbers were positive, and the number 0 would. 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 2500 BC, the symbol "0" was used in the Vedas, the oldest document in India. At that time, 0 indicated that India was short. 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 the nature of 0. Any number multiplied by 0 is 0, and any number plus or minus 0 gets any number. Unfortunately, he didn't mention the example of calculating with the symbol of life position. Some scholars believe that the birth and development of the concept of "0" in India is due to the philosophical thought of "absolutely nothing" in Indian Buddhism. In 733 AD, when an Indian astronomer visited Baghdad, the capital of Iraq, he introduced this notation to * * * people, because it was simple and easy to operate, and soon replaced the previous * * * numbers. This symbol was later introduced into western Europe.

4. What are the knowledge points about 0?

0 is neither positive nor negative, it is a natural number.

0 is even; Not a prime number or a composite number. 0 is the smallest complete square number.

The reciprocal of 0 is 0, that is, -0 = 0. The absolute value of 0 is itself, that is ∣0∣=0.

0 multiplied by any real number equals 0, divided by any non-zero real number equals 0, and any real number plus 0 equals itself. 0 has no reciprocal and negative reciprocal, a non-zero number divided by 0 has no meaning in the real number range, and 0 divided by 0 has infinite solutions.

The positive power of 0 is equal to 0, and the negative power of 0 is meaningless because 0 has no reciprocal. The power of 0 of any number except 0 is equal to 1 0. You can't do the base and real number of logarithm.

0 occupies a position in a multi-digit number. For example, 0 in 108 means that there are no ten digits, so you must not write 18. 0 cannot be used as a multi-digit most significant bit.

When 0 is not before other numbers, it means a valid number. The factorial of 0 equals 1.

0 is always the origin of the coordinate system. Zero is the dividing point between positive and negative numbers.

Any number *0 gets 0. 0 is a natural number at present.

The denominator in the score is 0, which makes no sense.

What is the role of 5.0 in mathematics?

The Work of "0" in Mathematics

"0" plays an important role in mathematics. Individually, 0 can mean nothing, and in decimals, 0 represents the boundary between decimals and integers; In the symbol, 0 indicates vacancy; Adding 0 after a non-zero integer is exactly 10 times of the original number ... Besides, 0 has special significance.

(1) indicates that there is no unit somewhere: for example, the "0" in 305 and 0.05 indicates that there is no unit somewhere.

(2) Indicates the starting point: for example, mark a "0" on the scale line at the starting point of the ruler.

(3) used for numbering: for example, 0068 will let people know that the largest number is four digits.

(4) Boundary: We often say that a certain temperature is 0 degrees Celsius and the height of the horizontal plane is 0 meters. Here, 0 degrees Celsius is not without temperature, and 0 meters is not without height; 0 is used here as a quantitative limit.

For example, the temperature above zero and below zero is bounded by "0"; Things are bounded by the origin "0"; Positive and negative are bounded by the neutral number "0".

(5) Indicates the accuracy: For example, 0.50 indicates that the accuracy reaches 1%.

(6) the need for bookkeeping; For example, 3 yuan is generally recorded as 3.00 yuan.

6. Mathematics in the first grade of primary school: What does 0 mean, what does it mean, what does it mean?

0 means "no", which may be the earliest meaning of 0 and the original meaning of 0.

If the inventory of a commodity is 0, that is, the commodity is no longer in this warehouse. But in addition to this meaning, 0 can also mean: ① Numbers.

For example, 10, 100 and so on. , where 0 has positional significance. ② Accuracy.

0.2, 0.20, 0.200, etc. , which means accurate to one tenth, one hundredth and one thousandth respectively. 3 dividing line.

For example, 0 degrees Celsius, which is the dividing line between the temperature above zero and the temperature below zero. ④ Critical point.

When the water temperature is 0 degrees, this is the key temperature for the mutual transformation between water and ice, and it is the critical point and junction point. It can be seen that 0 is not only meaningless, but also has many specific and clear contents, which are richer than other numbers.

As a math teacher, equating 0 with nothing will make a joke. If the lowest temperature is 0 degrees this morning, there will be no temperature this morning. Therefore, math teachers should not just stare at math textbooks, because there are many agreements on math knowledge in primary school textbooks, which are only suitable for primary school students to learn. If they get them outside the classroom, they will be incomplete. Therefore, math teachers should also learn more extracurricular knowledge of mathematics and prepare more math magazines or materials to expand their knowledge.

7. Tell me something about mathematics, about 200 words.

The history of zero

Mathematical historians call 0 "Columbus egg" not only because it looks like an egg, but also because it contains profound philosophy. Everything is difficult at the beginning, and some people are easy to imitate at the beginning. The appearance of 0 is a typical example. Before the invention, no one thought that once it existed, everyone would use a simple method to count it.

We know that zero is not only meaningless, but also has the following meanings; In the value system notation, zero represents "blank" and plays the role of indicating the position of the number. For example, 0 in 304 indicates that there are no digits in the ten digits; Zero itself is still a number, which can participate in the operation together with other numbers; Zero is the starting point or boundary of the scale, for example, time starts from 0.

In ancient Babylon, the zero sign of cuneiform characters played the role of zero sign in the current value system. On the one hand, it means zero, on the other hand, it also means the position of the number. However, they did not regard zero as a number, nor did they associate it with the concept of "nothing".

Indians' greatest contribution to zero is to admit that it is a number, not just a vacancy or nothing. Brahmagupta described the operation of zero completely: "negative negative zero is negative, positive and negative zero is positive, and zero negative zero has nothing;" : zero times a negative number, and a positive number or zero is zero. ..... zero divided by zero is nothing, and a positive or negative number divided by zero is a fraction with zero as the denominator. " Everyone who has studied division knows that zero cannot be divided, because if a≠0 and b=0, there can be no C to make BC = A. This truth is well known, but it has gone through a long history before the correct conclusion is reached.

China has been counting with counting chips since ancient times, and it has been counting with counting chips for a long time, adopting the decimal numerical system of 10. Babylon knew the value system, but it used the 60-based system. India did not have a clear notation of 10 decimal system on inscriptions until 595 AD. The value system must have a method to represent zero. At first, China used a space to represent zero, and later used a zero to represent zero. Later, Indian was introduced to China.

In our eyes, the existence of zero is so natural and concise, but even such a simple zero has such a complicated history.

8. What are zero numbers and non-zero numbers in common sense of mathematics?

The meaning of non-zero is the meaning of the word itself: a quantity that is not zero anywhere.

For example, in the expression+1, the answer will never be zero (even when; When c is zero or negative). The answer of the expression is called "zero" because if: C=0, the answer of the expression will "disappear" to zero.

? What are rational numbers, irrational numbers and real numbers? Rational numbers or fractions are usually considered as divisors of integers (i.e. ratios). By creating a fraction (dividing one integer by another), a rational number produces a divisible number or cyclic decimal.

For example, 2.05 equals 0.333 33. These are both rational numbers.

On the other hand, "irrational numbers" are all numbers that can be written as acyclic decimal and infinite decimal. Irrational numbers are also called irrational numbers, which include "row" (i.e. 3. 14 1.592 ...).

Finally, rational numbers and irrational numbers together form a "real number". Most of the numbers we use in our daily life are real numbers.