How to prove 1 1 2, how to prove 1 1

Please refer to the proof of mathematician Master Chen Jingrun... I can't prove it.

Please find a child in the first grade to prove it.

Set the first one to x

Then set the second one to y

So 1+1=x+y

Since 1=1, then x=y

So 1+1=x+x

Two x's are represented by two x's.

2×x=2x

Knowing that x=1 then 2x=2 1=2

Finally, 1+1=2

Let 1 be x and another 1 be y

then 1+1=x+y

Since 1=1, then x=y

Since x=y, then 1+1=x+x

x+x=2x

1+1=2x

x=12x=2×1

x=2, so 1+1=2

If you have one candy and your mom gives you another candy, then you have two sugars, right? Children.

Proof of 1+1=2:

The successor of 1+1 is the successor of 1, i.e. 3.

So the successor of 2 is 3.

According to Piano's axioms.

If b and c are both natural numbers.

a, then b = c; , the sedan hand can get: 1 + 1 = 2.

Because the successor of 1+1 is the successor of 1, i.e. 3.

Therefore, the successor number of 2 is 3.

According to Piano's axioms: if b and c are both successors of the natural number a, then b = c; , yields: 1+1=2.

An apple plus an apple is two apples.

Proof: a b a

a∩b＜b（a∩b）^c＞a^c

a∩b）^c>b^c

a∩b）^c＞a^c∪b^c……※

The same can be argued, (a b) c a c b c

Substitute a c into a and b c into b so that there is.

a c b c) c (a c) c (b c) c=a b on both sides, get.

a^c∪b^c＞（a∩b）^c

i.e. (a b) c a c b c

Combined with the equation, it can be obtained, :(a b) c = a c b c mathematical set is a fundamental concept mathematically. A basic concept is a concept that cannot be defined by other concepts, nor is it a concept that cannot be defined by other concepts.

The concept of a set can be developed in an intuitive, axiomatic way"Definitions"。

Set (abbreviated set) is a basic concept in mathematics and is the object of study of set theory, which was not created until the 19th century. In the simplest terms, it is defined in the most primitive set theory, naïve set theory, and a set is"A bunch of stuff"。collection"stuff", called an element.

If x is an element of the set a, it is denoted as x a. A set is a collection of certain distinguishable objects in people's intuition or thinking that merge together to form a whole (or monomer), and this whole is a set. Those objects that make up a set are called elements (or simply metas) of the set.

Modern mathematics is still used"Axiom"to prescribe the collection. The most basic axioms are examples: axioms of extension:

For any set s1 and s2, s1=s2 if and only if for any object a, if a s1, then a s2; If a s2, then a s1. There is an axiom of disorder for sets: for arbitrary objects A and B, there is a set S, such that S has exactly two elements, one for object A and one for object B.

By the axioms of extension, the set of disordered pairs composed of them is unique and denoted as. Since a and b are any two objects, they may or may not be equal. When a=b, , can be denoted as or, and is called a set of units.

An empty set existentially axioms: there exists a set, which does not have any elements.

At present, no one can prove it, and this can only be memorized as common sense.

Set the first one to x

Then set the first 2 oaks to y

So 1+1=x+y

Since 1=1, then x=y

So 1+1=x+x

Two x's are represented by two x's.

2×x=2x

Knowing that x=1 then 2x=2 1=2

Finally, the early chain is 1+1=2

1+1=(2-1)+(2-1)=2(2-1)=2( 2 -1 )=2( 2 -1 +2 2-2 2+1-1)=2( 2-1) +2(2 2-2)=2(2-2 2+1)+2(2 2-2)=4-4 Kuanhe 2+2+4 2-4=2 This is a difficult proof question in Xingyuan, and the derivation process is very cautious and complicated.

As for why 1 plus 1 is equal to 2, because 2 is defined as 1+1, that is, 2=1+1, according to the principle of equation interchange, left and right interchange, the equation still holds, so it can be obtained as follows, 1+1=2.

Piano's axioms.

The Piano axioms, also known as the Piano axioms.

It is a system of five axioms about natural numbers proposed by the mathematician Piano (Piaro). According to these five axioms, a first-order arithmetic system, also known as the Piano arithmetic system, can be established. These five axioms of Piano are described in a non-formal way as follows:

1 is a natural number; For every definite natural number a, there is a definite successor a' ，a'It is also a natural number (the successor of a number is the number immediately following this number, e.g., the successor of 1 is 2, the successor of 2 is 3, and so on); If b and c are both successors of the natural number a, then b=c; 1 is not a successor to any natural number; Any proposition about a natural number can be proved to be true to n if it is proved to be true to the natural number 1 and assumed to be true for the natural number n'It is also true, then, that the proposition is true for all natural numbers. (This axiom, also called the inductive postulate, guarantees mathematical induction.)

Note: The inductive postulate can be used to prove that 1 is the only natural number that is not a successor, because if the proposition is "n=1 or n is the successor of other numbers", then the condition of the inductive postulate is satisfied. If 0 is also considered a natural number, then the axiom 1 is replaced by 0.

A more formal definition in this paragraph.

A Dedekin-Piano structure is a triplet that satisfies the following conditions.

x, x, f): 1. x is a set, x is an element in x, and f is the mapping of x to itself; 2. x is not in the range of f.

Inside; 3. F is a single shot. 4. If a is a subset of x and satisfies that x belongs to a, and if a belongs to a, then f(a) also belongs to a, then a=x. This structure is similar to the set of natural numbers derived from Piaro's axioms.

The basic assumptions of the union are the same: 1. p (set of natural numbers) is not an empty set.

2. One-to-one mapping of the direct successor elements of A->A in P to P; 3. The set of subsequent element mapping images is a true subset of p.

4. If any subset of p contains both elements that are not successor elements and successor elements that contain each element in the subset, then this subset coincides with p. It can be used to prove many common theorems that are not known to them! For example:

The fourth hypothesis is the theoretical basis for the first principles of the widely used inductive method (mathematical induction).

This is the theoretical basis of the addition of numbers: of course this is based on people's experience 1+1=2 1+2=3....Later, a theory was established in order to strengthen the theoretical foundation, which became the theoretical basis of the addition of natural numbers.