From the Continuity Problem of Set Potential to Georg Cantor Conjecture

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.


Cantor's Famous Conjecture Is Whether There Is Continuity Between the Potential of Natural Number Set and That of Real Number Set
Further proof on the continuity of set potential. 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. Cantor put forward his famous conjecture that the above X set does not exist.
In order to study continuity of set potential between the natural number set and the real number set, four mixed potential are formed, which belong to the category of transfinite theory and are discontinuous set potential. The connection in the complexity of human genes is formed by the continuity of set potential. It is found that the complex pairing of genomes also has weak order and law, the continuity and controllability of the whole pairing potential of gene chain, and the discontinuity of DNA gene fragment, and the continuity of DNA forming chromosome skeleton to life body, so as to ensure the relative stability of species.

The continuity Problem of Proving Set Potential in Detail
Sets , , potential , and The potential of the set of is All X sets satisfy ∼ 0 ∼ 1, It is not stable, so there is no relation between the potential of natural number set N and real number set R that is ∼ 0 ∼ 1. Subsets of set N of natural numbers 0,1,2,3,4,5 , Subsets of real set R set 0,1,1.5,2,3,4,4.1,5 , ! Sets " 0,1,2,3,4,5 , " ! , , " All known as, A is the potential of N set, B is the potential of R set, C is the potential of N set.

See axis below
, ", potential a , ", One to one corresponding subset, and a, c are natural numbers.
Further analyze (2) and sort out the formula.
∀@∪B∆ . / is a continuous potential, that is, the potential of N (set of natural numbers).  ∴∼ 0 < <∼ 1 not established That is, the potential element of the set of 2, ∼ 0 ∈ natural numbers set in ∼ 0; and the unit of the potential of 2, ∼ 1 ∈ ! real number set in ∼ 1.
∼ 0 → 2 ≠∼ 1 → 2, that is 2 ≠ 2 * . It shows that the set potential has a great influence on the meaning of numbers.
According to the property (24) formula, it can be deduced from the potential of natural number set and real number set.
2 ∀2 → ∀ → 2 , that is 2 2 → 2 * ; ∀2 ∈∼ 0, ∀ → 2 ∈∼ 1 According to (24) and (25), we can know whether there are two 2 in the potential of natural number set. Whether there are two 2 * , in the potential of real number set. Their relationship: 2 2 → 2 * . There are two 2 potentials in a natural set. They are different. They are called:2 → ; 2 ← . There are two 2 potentials in the real number set. They are different.
Passing to the limit in the right-hand side of (27), we infer In (28), ↑ is the limit potential of mixing, ↓ is the limit potential of mixing. And simplify it. On the extension of the meaning of the potential of (30) infinite partition class, it embodies the symmetry relation that the smallest element after infinite partition is 2.
The meaning of this pattern is far-reaching.

There Is No Continuity Between Potential of the Natural Number Set and the Real Number Set
The smallest element after infinite partition is 2, which forms four mixed potentials. The smallest element is infinitesimal of infinitesimal, which belongs to the category of transfinite theory. Georg Cantor's conjecture about the continuity of set potential is proved.

The Infinite Partition Class and the Continuity Problem of Set Potential Is Constructed by Differential Incremental Equilibrium Theory
Through the limit potential of differential increment, four mixed potentials with infinitesimal minimum element are formed. That is, + Y34 D N∆↑ ↓ . / W ∆ is always accompanied by potential. So + Y34 D N∆↑ ↓ . / W ∆ is a discontinuous potential. Cantor's conjecture is proved that the potential of the set of natural numbers and the set of real numbers is discontinuous.