The development of number is almost blasphemous for the abbreviation of the history of number development! When, where and how did natural numbers, integers, rational numbers, irrational numbers, imaginary numbers, real numbers and complex numbers come into being? Evolution? Like most mathematical concepts, their evolution is carried out in a certain field of thinking, which is either accidental, inevitable, unfamiliar or necessary for exploration. It is hard to imagine whether we should limit all kinds of problems to a special set of numbers when trying to solve them. We admit that many problems are confined to a specific scope or area, which makes it accompanied by a specific set. But at least know the existence of other types of numbers in the solution. Such a problem happens to be an exercise. Although we have all the complex numbers in our hands now, we might as well imagine dealing with such a problem, that is, finding the value of x in the equation x+7 = 5, but we don't know the negative number. What will happen at this time? -This question is flawed! -Nobody answered! -The equation is incorrect! (1) Original note: Arabic textbooks introduce negative numbers into Europe. But in the centuries of 16 and 17, European mathematicians were unwilling to accept these numbers. N Chukuyt (15th century) and M Stiddle (16th century) classified negative numbers as absurd. Although j cardin classified negative numbers, etc. Fortunately, there are some brave and confident mathematicians who are willing to take risks and firmly believe that the solution exists in the field of undiscovered numbers. Finally, they take a step and specify a new set of numbers besides the original ones. It is conceivable how exciting and unusual it is to create a negative number to solve the above problems. Equally interesting is the verification of the new number. See if it also follows the axiom of the set of existing numbers. It is almost impossible for us to spend all our time on the origin of different numbers, but we can imagine similar problems and the outline of new number discovery. For many centuries, people all over the world only used natural numbers. At about that time, they had no other needs. Of course, each of them wrote symbols and systems of natural numbers. It changes with different cultures. The first zero can be traced back to the second Millennium and appeared on the clay tablet in Babylon. It was originally empty, and later it was represented by two symbols or zero. But here zero is more as a position holder than a number. The Mayan and Indian digital systems first regarded zero as the number zero. As the holder of position, rational number is the second stage of evolution. People need to allocate a whole quantity, just like dividing a piece of bread. Although there are no design symbols to represent these numbers, ancient people knew the existence of fractions. For example, the Egyptians used "mouth" to write, and the Greeks used the length of line segments to express different quantities. They know that the points on the number axis are not only occupied by natural numbers and rational numbers. At this time, we found the intervention of irrational numbers. Rectangular. Needless to say, we know that people have used irrational numbers at that time. History shows that in the process of discovering new numbers, solving old problems and generating new ones happen at the same time. It is one thing to find a new number set, but its definition and logical system must be acceptable, and it should be compatible with some rules adopted in many years of evolution. (② Original note: At that time, the logical basis of integers, rational numbers, irrational numbers and negative numbers had not been established. India and Arabs use these numbers at will in their calculations. They use positive and negative numbers as the values of assets and liabilities. Their work mainly focuses on calculation, and they don't care much about their geometric validity. This is because their arithmetic does not depend on geometry. ) Negative numbers were once unacceptable to European mathematicians. This state even lasted until the17th century. If the application of square root is not limited to non-negative sets, then the formula equation requires the application of imaginary numbers in its solution. One of the equations is x2 =- 1. Design a universal set and connect all the numbers together, thus introducing the complex number, which appears in the quadratic equation x2+2x+2 = 0. It can be regarded as a category of complex numbers. For example, a real number is a complex number whose imaginary part is 0, and a pure imaginary number is a complex number whose real part is 0 but whose imaginary part is not 0. When described by geometry, imaginary and complex numbers become more specific. Just as the ancient Greeks described real numbers on the number axis, complex numbers can also be described by complex planes. Each point on the complex plane corresponds to one and only one complex number, and vice versa. The five solutions of the equation x5= 1 can be represented graphically. Since complex numbers can be described by two-dimensional points, there seems to be a logical transition problem, that is, what kind of numbers can describe points in high-dimensional space. We found a number called quaternion, which can be used to describe four-dimensional space. Now the remaining question is-does the number stop here? We say that with the development and application of new mathematical ideas, new numbers will often be produced! References:

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