1 and the generation of 0. It may be interesting to talk about some history. Mathematics begins with counting, which was called "knotting notes" in prehistoric times. Even before that, humans had no writing. If there is anything, they tie a knot with a rope. This is the origin of numbers, such as 1, 2, 3, etc. And integers. Integers are added, subtracted, multiplied and divided to produce decimals (including cyclic decimals). Later, the Pythagorean theorem (Pythagorean theorem) in ancient Greece was produced. However, 0 was not created by Arabs until 1500 years ago. If human history is counted as 5000 years, it will take 3500 years to produce 0, which is a great event in the history of mathematics. Now we turn 0-9 into Arabic numerals to record the great contribution of Arabs. Because of the generation of 0, the carry problem is solved and the calculation is simple. We know that 1-9 means that there is an actual rope to tie, and it makes people feel that there is nothing listed in the number, and it can't be done without extraordinary wisdom.

The origin of 2.0/0. First of all, thinking that 0/0 is the basis of the development of calculus. We study math step by step. Elementary school courses are called arithmetic, middle school students learn algebra and geometry, high school students learn function and analytic geometry, and college students learn advanced mathematics, which is actually calculus. This kind of calculus was pioneered by Newton and Leibniz 300 years ago. Because of the knowledge of calculus, Newton proved the theorem of universal gravitation by elliptic integral method. Therefore, we often hear Mr. Hua say that "mathematics is the jewel in the crown of the goddess of science", which is what Mr. Hua wrote in the preface when he wrote Number Theory.

The mathematical meaning of 3.0/0. In elementary school arithmetic, we can understand that 0 cannot be a divisor, because the calculation of arithmetic needs a unique numerical result, but the result of 0/0 is an uncertain number. Understanding the meaning of 0/0 is beyond the scope of arithmetic, so it is meaningless to say 0/0 directly in primary school textbooks. It is simple and direct, which is enough for students who only study arithmetic. For example, arithmetic is China. I live and work in China, so I don't need to know anything outside China. But if I go out of China, I will find that I still have new knowledge.

4.0/0 philosophical thinking. Philosophy is knowledge about what life is and what the world is. Does it have anything to do with 0/0? That's true. We know that mathematics is a logical knowledge, first of all, axioms, from which theorems are derived and problems are solved by theorems. Axiom cannot be deduced, which is an inevitable truth that people have summed up from practical experience. This is, of course, that human understanding of the world (philosophical thinking) is described in mathematical language, and the problem solving of axiomatic deduction theorem is also in accordance with philosophical thinking mode, because logical reasoning is also defined in philosophy, such as syllogism (for example, everyone has two legs, so Zhang San has two legs). In ancient times, mathematicians were first philosophers, such as Pythagoras, and there was Pythagoras School in ancient Greece, which was an influential school of philosophy at that time. Everyone in this school has the same way of life. Here is an interesting story. Pythagoras himself denied the existence of irrational numbers. One of his students used the teacher's theorem to prove the existence of irrational numbers, which was a betrayal of his legacy at that time. In order to survive, students had to flee to Italy. Do you know the original title of Newton's three laws of mechanics? A mathematical principle called natural philosophy. It is interesting that most scientists 300 years ago were philosophers. To understand the practical significance of 0/0, we can't just think about it mathematically. Its origin lies in philosophy. The mathematical solution of 0/0 is a symbol, which is indefinite, endless and cyclical. It is also meaningful to understand our world with mathematical concepts, but people's general thinking is linear, and the reciprocal is continuous according to 1, 2,3, so it is difficult to understand the concepts of uncertainty, infinity and cycle between squares. China's Book of Changes is also a mathematical science, and this 0/0 has something in common with it.

4. The humanistic spirit of mathematics. The mathematical story mentioned above is actually to tell you that mathematics is not only a scientific tool, but also a humanistic spirit. The Book of Changes begins with "Tai Chi is infinite, and Tai Chi gives birth to two instruments". You see, first 0, then 1, then 2, and then there are many strange operations, which I don't understand.

I also tell a story about Newton. When I was studying politics in junior high school, I first talked about dialectical materialism. In the course, I first define: the world is material, material determines consciousness, and material is moving. There is a lot of space in the course to criticize the idealistic world in which consciousness determines material views, and to criticize Newton for saying that "material movement is driven by God". I didn't understand it at that time anyway, so recite it. The books I read later really did. After Newton put forward the three laws of mechanics and gravitation, someone asked Sir Newton, "Why does the earth revolve around it? Where does the driving force of the origin of the universe come from? " Sir Newton replied that God pushed it with a finger. It is not surprising that Sir Newton believed in God in the18th century, and his answer is not necessarily wrong. I think people who can think and calculate 0/0 must be extraordinary and empathetic. Personal understanding of the concept and control of 0/0 is within the scope of God in the West, and it is solved by the Book of Changes in the East. This kind of knowledge is inexhaustible for human beings. It's hard to understand, calculation and control are extremely difficult and almost impossible.

This is the answer of 0/0.