A REAL NUMBER AS ONE OF THE STATES OF ITS ABSOLUTE VALUE

The article raises the following question. How to explain the equivalence of the whole set of real numbers and its correct part? Our most general conceptual answer to the question posed: the whole infinite set |А| and its correct part |В| can be equivalent only in the case of the existence of an equally powerful set |C| , the elements of the system of which are in a state of superposition with respect to the elements of the sets |A| and |B|. The universal principle of the superposition of the module of a real number is formulated and justified: the absolute and variable magnitude of any real number is in a state of superposition with respect to the numerical line and the effect of the mathematical system of absolute quantities is the set of all real numbers.