**Author details**

scientists" that had no connection with reality. And these natural numbers set up such a trick. If you look at Fermat's theorem from this position, a whole series of

• How many solutions will there be if we allow fractional degrees?

• Will there be solutions to the equation if, for the third power, the third term is

• Is it possible for fractional numbers to find the same condition connecting

in our three-dimensional space, and in the third degree there are no solutions

Is it a coincidence that for the second degree, three variables still give solutions

So, to summarize this replica, it can be argued that this condition (in Fermat's theorem) connects three independent variables and their nonlinear transformations defined by the fourth variable, the degree, and it is the discreteness of all variables

This relationship of the dimension of equations and the nonlinearity of transformations with the discreteness of variables is, in the opinion of the author of the article, the main meaning of Fermat's paradox and one more confirmation of the

The problem of discreteness in science and technology is one of the most inter-

At different stages of development, either discreteness or continuity began to

So, integral and differential calculi replaced arithmetic and algebra, connecting all quantities with continuous operations and conditions. Then quantum physics

The theory of stability, as the basis of cybernetics, was supplemented by discrete controls and methods, and this chapter has shown how the influence of discrete elements can be taken into account by links with continuous frequency characteristics. It is also shown how frequency analysis can well take into account the discreteness of some elements of self-propelled guns and obtain fundamentally new

questions will arise.

*Control Theory in Engineering*

already?

**10. Conclusion**

replaced the classical one.

types of correction and new results.

esting.

**344**

added to the left side?

• Or fractional variables?

And so many others ...

several variables by impossible equations?

that makes this simple equation (or formula) impossible.

fundamental concept of discreteness [21].

prevail and became a new word in science.

Vladimir Kodkin South Ural State University (National Research University), Chelyabinsk, Russia

\*Address all correspondence to: kodkina2@mail.ru

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
