The barber's paradox is similar to the paradox put forward by the famous mathematician Bertrand Russell (1872- 1970): there is a barber in a certain city, and his advertising words are written like this: "My haircut skills are superb and the whole city is famous. I will shave all the people in this city who don't shave themselves. I will only shave these people. I would like to extend a warm welcome to everyone! " When people come to him to shave, they naturally don't shave themselves. One day, however, the barber saw in the mirror that his beard had grown. He instinctively grabbed the razor. Do you think he can shave himself? If he doesn't shave himself, then he belongs to the "person who doesn't shave himself" and he has to shave himself. What if he shaved himself? He belongs to the "person who shaves himself" and should not shave himself. What is paradox? Let's first understand what paradox is. Paradox comes from the Greek word "para+dokein", which means "think more". The meaning of this word is rich, including all mathematical conclusions that contradict human intuition and daily experience, and those conclusions will surprise us. Paradox is a contradictory proposition. That is, if this proposition is admitted, it can be inferred that its negative proposition is established; On the other hand, if we admit that the negative proposition of this proposition is true, we can deduce that this proposition is true. If we admit it is true, after a series of correct reasoning, we can conclude that it is false. If you admit that it is false, after a series of correct reasoning, it is true. There are many famous paradoxes in ancient and modern China and abroad, which have impacted the foundation of logic and mathematics, stimulated people's knowledge and precise thinking, and attracted the attention of many thinkers and enthusiasts throughout the ages. Solving paradoxes requires creative thinking, and the solution of paradoxes can often bring people new ideas. There are three main forms of paradox: 1 An assertion seems to be definitely wrong, but it is actually right (paradox). 2. An assertion seems to be definitely right, but it is actually wrong (specious theory). A series of reasoning seems impeccable, but it leads to logical contradictions. If everyone is regarded as a set, then the elements of this set are defined as the objects of tonality. Then, the barber claimed that his elements were all the collections in the city that did not belong to him, and all the collections in the city that did not belong to him. So does he belong to himself? Thus, Russell's paradox is obtained from Barber's paradox. The same is true of reverse transformation.