In the process of solving the roots of higher-order equations, it is found that the numbers with multi-layer radical forms obtained by special methods are not the roots of the equations, but only the approximate values of the roots of the equations. It is found that the numbers formed by the square root of non-rational numbers are inaccurate numbers. Among them, quantum numbers can be directly proved to be unordered. Further research has found quantum superposition numbers. This new discovery breaks the view that "numbers are accurate". New research shows that the rational numbers in the real number system have some non-rational counterparts. The non-rational numbers are those that cannot be expressed as ratios of integers but are roots of polynomials with rational coefficients.The numbers with double-layer square roots obtained by solving the equations by the Cardan method are inaccurate numbers. They are not real numbers under the classical definition, but only approximate values of the roots of the equations. The mainstream view is that the roots of the equations belong to the real numbers under the classical definition, which proves the general formula that there are no roots for cubic equations of one variable, and at the same time proves that the Galois group theory is wrong in its discussion of the roots of equations. In the function of finding non-trivial zeros in the Riemann hypothesis, there are a large number of square roots of transcendental numbers π, which are similar to multi-layer radical numbers. These numbers are not real numbers under the classical definition, and have no accurate values. After participating in the operation, the calculation results must not be zero. Therefore, it can be proved that there is no "non-trivial zero point" and no polynomial root with a real part value of 1/2, which negates the Riemann hypothesis.The discovery and proof of quantum numbers and quantum superposition numbers have broadened human thinking about the nature of nature. It provides a reference for human understanding of the behavior of the microscopic world, making our understanding of mathematics, physics and even the entire universe more profound and comprehensive. The discovery and proof of quantum numbers and quantum superposition numbers reveal the ultimate mystery of the universe. That is, some laws of the universe cannot be perfectly expressed by functions, nor can they be accurately expressed by mathematical formulas. Some conclusions derived from quantum numbers are consistent with current quantum theory.