The "1+1" studied by Chinese mathematician Chen Jingrun is not 1+1 in arithmetic. Many people also mistakenly think that Chen Jingrun is studying why 1+1 is equal to 2. The algorithm is defined by humans and does not need to be studied. The "1+1" researched by Chen Jingrun is actually synonymous with Goldbach's conjecture.
Mathematically, the very famous "(1+1)" is the famous Goldbach conjecture. In order to break this conjecture, we need to prove "1+1=2".
In the 18th century, the German mathematician Goldbach accidentally discovered that every even number not less than 6 is the sum of two odd prime numbers. For example 3+3=6; 11+13=24. He tried to prove his discovery, but failed repeatedly.
In 1742, the helpless Goldbach had to ask Euler, the most authoritative Swiss mathematician in the world at that time, to put forward his conjecture. Euler quickly wrote back that the conjecture must be true, but he could not prove it.
Someone immediately checked the even numbers greater than 6, and it was counted to 330,000,000. The results showed that Goldbach's conjecture was correct, but it could not be proved. So this conjecture that every even number not less than 6 is the sum of two prime numbers [referred to as (1+1)] is called "Goldbach's conjecture",
At the end of 1956, the mathematician Chen Jingrun, who had written more than 40 papers successively, was transferred to the Academy of Sciences and began to concentrate on number theory under the guidance of Professor Hua Luogeng. In May 1966, he rose like a bright star in the sky of mathematics, announcing that he had proved (1+2), that "sufficiently large even numbers can be expressed as a prime number and a number with no more than two prime numbers. The sum of the products."
Extended information:
Peano's five axioms are stated informally as follows:
①0 is a natural number;
②Every definite natural number a has a definite successor number x', and x' is also a natural number (the successor of a number is the number immediately after the number, for example, the successor of 1 is the successor of 2 and 2 The number is 3, etc.);
③ If b and c are both successors of the natural number a, then b = c;
④0 is not the successor of any natural number;
⑤ Let S be a subset of the set of natural numbers, and (1) 0 belongs to S; (2) If n belongs to S, then n' also belongs to S.
(This axiom is also called the axiom of induction, which guarantees the correctness of mathematical induction)
A more formal definition is as follows: A Dedekind-Piano structure is a triple (X, x, f) where X is a set, x is an element of X, f is a mapping of X to itself, and meet the following conditions:
x is not in the range of f;
f is a single shot;
If x∈A and "a∈A implies f(a)∈A", then A=X.
The basic assumptions about the set of natural numbers introduced by this structure:
1. N (set of natural numbers) is not an empty set;
2. There is a one-to-one mapping of a→a' from N to N;
3. The set of images mapped by subsequent elements is a proper subset of N, in fact, N\{1} (or N\{0});
4. If a subset P of N contains both non-successor elements and successor elements that contain each element in the subset, then this subset is equal to N.
Proof of 1+1:
The successor of ∵1+1 is the successor of the successor of 1, which is 3,
The successor of ∴2 is 3.
According to Peano's axiom ③, we can get: 1+1=2.