From the Continuity Problem of Set Potential to Georg Cantor Conjecture

Abstract

Background in 1878, Cantor puted forward his famous conjecture. Cantor's famous conjecture is whether there is continuity between the potential of the set of natural numbers and the potential of the set of real numbers. In 1900, Hilbert puted forward the first question of 23 famous mathematical problems at the International Congress of mathematicians in Paris. Purpose To study the continuity of set potential between the natural number set and the real number set, so as to provide mathematical support for the study of male gene fragment in human genome. Method The potential is extended by infinite division of sets and differential incremental equilibrium theory. There is a symmetry relation that the smallest element of infinite partition is 2. When a set A corresponds to a subset of a set B one by one, but it can't make A correspond to B one by one, the potential of A is said to be smaller than that of B. If a is the potential of A, and b is the potential of B, then a < b. We use ∼•0 to express the potential of natural number set and ∼•1 to express the potential of real number set. At present, it is not known whether there is a set X, the potential of X satisfies ∼•0 < x < ∼•1. Results There is no continuity problem in the set potential of the natural number set and the real number set, and four mixed potentials can be formed. It belongs to the category of super finite theory. Conclusion Cantor's conjecture is proved that potential of the natural number set and the real number set. That is, the potential of X satisfies ∼ 0 < x < ∼ 1 does not exist.