Why is one plus one equal to two

Chen Jingrun, a Chinese mathematician, studied “1+1” Not arithmetic 1+1, Many people also mistakenly believe that Chen Jingrun is studying 1+1 Why is it equal to 2, Algorithms are defined by humans , There is no need to study . Chen Jingrun studied “1+1” In fact, it is synonymous with Goldbach's conjecture .

The math , Very famous “（1+1）”, It is the famous Goldbach conjecture . To break this conjecture , Need to prove “1+1=2”.

18 Century time , German mathematician Goldbach accidentally discovered , Each is not less than 6 Even numbers of are the sum of two odd primes . for example 3+3=6; 11+13=24. He tried to prove his discovery , But repeatedly defeated .

1742 year , In desperation, Goldbach had to turn to Euler, the most authoritative Swiss mathematician in the world at that time , Put forward his own conjecture . Euler wrote back soon and said , This conjecture must be true , But he can't prove .

Someone immediately responded to one by one 6 The even number of , Until 330000000, The results show that Goldbach's conjecture is right , But it just can't prove . So each of this road is no less than 6 Even numbers are the sum of two prime numbers [ abbreviation （1+1）] guess , This is called “ Goldbach conjectures ”,

1956 end of the year , Chen Jingrun, a mathematician who has written more than 40 papers, was transferred to the Academy of Sciences , He began to study number theory under the guidance of Professor Hua Luogeng .1966 year 5 month , He rose to the sky of mathematics like a bright star , Declare that he has proved （1+2）, namely “ A sufficiently large even number can be expressed as the sum of a prime number and a product of no more than two prime numbers ”.

Extended data ：

Piano's five axioms are described in a non formal way as follows ：

①0 It's a natural number ;

② Every definite natural number a, There is a definite successor number x' ,x' It's also a natural number （ The subsequent number of a number is the number immediately after this number , for example ,1 The successor number of is 2,2 The successor number of is 3 wait ）;

③ If b、c All natural numbers a The number of successors to , that b = c;

④0 Not the successor of any natural number ;

⑤ set up S Is a subset of the set of natural numbers , And （1）0 Belong to S;（2） If n Belong to S, that n' Also belong to S.

( This axiom is also called inductive axiom , It ensures the correctness of mathematical induction )

A more formal definition is as follows ： 　 A dadkin - The piano structure is such a triple (X, x, f), among X It's a collection ,x by X One of the elements ,f yes X Mapping to itself , And meet the following conditions ：

x be not in f Within the range of ;

f For a single shot ;

if x∈A And " a∈A  implication  f(a)∈A", be A=X.

The basic assumptions about the set of natural numbers derived from this structure :

1、N( Set of natural numbers ) Not an empty set ;

2、N To N In memory a→a' One by one mapping of ;

3、 The set of images mapped by subsequent elements is N The proper subset of , In fact N\{1}（ or N\{0});

4、 if N Subset P Elements that contain both non successor elements , There are also subsequent elements that contain each element in the subset , Then this subset is related to N equal .

1+1 The proof of ：

∵1+1 The successor number of is 1 The successor number of , namely 3,

∴2 The successor number of is 3.

According to piano's axiom ③, Available ：1+1=2.