Читать книгу All sciences. №1, 2022. International Scientific Journal - Ibratjon Xatamovich Aliyev - Страница 6

Aripova Sayera Bahodirovna, teacher of secondary school No. 1

Secondary School No. 1, Fergana, Uzbekistan

E-mail: karimov.1949@internet.ru

Annotation. Since ancient times, people have used the counting system to solve life problems of various types and characteristics, as a result of which they had to deal with the concept of real-natural numbers, and after working with tasks related to squares, they had to deal with tasks related to fractional numbers, already entering the rational set of numbers.

Keywords: inertial numbers, intentional mathematics, relativistic physics, sets of numbers, infinity.

Аннотация. С древних времён люди использовали систему счёта для решения жизненных задач различного типа и характеристик, в результате чего приходилось сталкиваться с понятием действительных-натуральных чисел, а после работы с задачами, связанными с площадями, приходилось сталкиваться и с задачами, связанными с дробными числами, входя уже в рациональное множество чисел.

Ключевые слова: ингенциальные числа, ингенциальная математика, релятивистская физика, множества чисел, бесконечность.

And when I already had to enter into the tasks related to the description of the circle, I had to face the first irrational number, after which their number began to increase and increase, creating already a lot of irrational numbers. It would seem that these real numbers, along with negative ones, which have also entered science, make up a full-fledged set of real numbers, quite sufficient to describe the outside world. What a surprise it was when I had to face the solution of equations of degree 3, which today are known as equations that have found a solution by the Cardano method. It was noteworthy that when solving these equations, one had to deal with the case of the presence of a complex unit or, more precisely, complex numbers – negative numbers under the radical.

And although this kind of numbers did not take root for a long time, but the discovery of this kind of numbers in the most fundamental processes of today’s world, namely as one of the solutions to the Schrodinger equations – equations describing any microobject simply forced us to accept this new kind of numbers and move on, exploring a variety of operations related to complex numbers and their derivatives.

Thus, a new set was discovered, which includes all of the above sets, that is, natural, rational, irrational and real sets, such a set was called complex.

Consequently, in order to arrive at obvious mathematical paradoxes and amazing phenomena, it is necessary to proceed from a physical phenomenon that was previously published in 1905 in Albert Einstein’s article “On the electrodynamics of moving bodies”, which was also based on the transformation of X. Lorenz, the works of J. Larmor, Henri Poincare and others. Initially, it is enough to use the famous conclusion (1.1), which goes to (1.2).

This equality has a deep physical meaning, but if we consider it as a function, then we can consider 3 cases:

1. If the speed of the body is less than the speed of light;

2. If the speed of the body is equal to the speed of light;

3. If the velocity of the body is greater than the speed of light.

Thus, 4 types of numbers are obtained from these 3 cases. The first one is real numbers, and the second one is complex numbers. This is followed by two previously unknown types of numbers, namely numbers that can be divided by zero, as well as numbers that are larger than this type of numbers.

And of course, progress does not stand still, and today various physical phenomena have already been investigated and discovered, still awaiting their explanation and mathematical interpretation. A striking example is the phenomenon of entangled particles, that is, it is a phenomenon in which two entangled leptons are formed, namely two electrons or photons, information about the spin of which is transmitted after determining or changing the spin of one to the other at a speed much higher than the speed of light – 3 case.

Also, the very fact of the presence of light waves, also known as photons in the form of corpuscles, makes one think about the moment when the speed of an object would become equal to the speed of light – 2 case.

And to describe all these phenomena, it became necessary to create a new section of mathematics, known as “Ingential Mathematics”, from the Latin ingens – “huge”. In this case, the presence of an exponential unit is assumed, that is, a fraction of one by zero, after which various arithmetic, algebraic and other types of operations are formed, converting both trigonometric, logarithmic, inversely trigonometric and other functions, and introducing completely new types of operations.

But before proceeding to the third case, it is worth clarifying that due to the derivation of the main energy function, the location of the exponential numbers on the numerical axis is determined, namely, these numbers are large infinity, which means it is the vertex of all sets, covering each of them, including the complex set. It is also determined that the complex numbers are the smallest and are already between the intervals of natural numbers. It is also possible to define the third kind of numbers as fractions of a unit and a complex number. At the same time, these types of numbers are called per-ingential from the Latin per-ingens – “super-large”. This type of numbers is even larger than the exponential numbers and has even more fascinating properties that have yet to be explored in more detail, however, like all the others.

List of literature

1. Balk M. B., Balk G. D., Polukhin A. A. Real applications of imaginary numbers. – Kiev: Radyanka school, 1988. – 255 p.

2. Bronstein I. N., Semendyaev K. A. Handbook of mathematics for engineers and students of higher education institutions. – ed. 13-E. – M.: Nauka, 1985. – 544 p.

3. Bugrov Ya. S., Nikolsky S. M. Higher mathematics. Volume one: Elements of linear algebra and analytic geometry. Moscow: Bustard, 2004. – 288 p.