  We discuss the procedure of different partitions in the finite set of $N$
integer numbers and construct generic formulas for a bijective map of real
numbers $s_y$, where $y=1,2,\ldots,N$, $N=\prod \limits_{k=1}^{n} X_k$, and
$X_k$ are positive integers, onto the set of numbers
$s(y(x_1,x_2,\ldots,x_n))$. We give the functions used to present the bijective
map, namely, $y(x_1,x_2,...,x_n)$ and $x_k(y)$ in an explicit form and call
them the functions detecting the hidden correlations in the system. The idea to
introduce and employ the notion of "hidden gates" for a single qudit is
proposed. We obtain the entropic-information inequalities for an arbitrary
finite set of real numbers and consider the inequalities for arbitrary
Clebsch--Gordan coefficients as an example of the found relations for real
numbers.
