[Ultimate Mathematical Problem] Please prove 1+ 1=2.

1+ 1=2? Don't underestimate this formula. 1+ 1=2 is one of the greatest formulas in science. Many people may ask, "Why 1+ 1=2?" This seems to be redundant (! ? ) problem. Now I'm trying to briefly introduce to interested netizens how to prove the mathematical statement "1+ 1=2" within the framework of axiomatic theory, which is "irrefutable" for most people. First of all, we should know that in the context of * * * theory, the objects we are discussing are all kinds of * * * (or classes, and the difference between them and * * * is not superfluous here), so the natural numbers we often encounter are also defined by * * * (or classes) here. For example, we can define 0, 1 and 2 (for example, qv. Quine) in the following way.

mathematical logic

Revised edition.

Chestnut 6

43-44):0:= { x:x = { y:~(y = y)} } 1:= { x:y(yεx . & amp； . x \ { y }ε0)} 2:= { x:y(yεx . & amp； . X \ {y} ε 1)} [For example, if we take an element from a molecule that belongs to the category of 1, then this molecule will become zero. In other words, 1 is a class composed of all classes with only one element. Now we generally use the method mainly introduced by von Neumann to define natural numbers. For example: 0: = λ

1:= {Λ} = {0} =0∪{0}

2:= {Λ

{Λ}} = {0

1} =1∨ {1} [λ is an empty set] Generally speaking, if we have constructed the set n,

Then its successor n * is defined as n ∨{ n}. In the general axiom system of * * * (such as ZFC), there is an axiom to ensure that this construction process can continue continuously, and all * * * obtained by this construction method can form a * * *, which is the so-called infinite axiom (of course, we assume that other axioms (such as the union axiom) have been established. Note: Infinite axioms are some so-called illogical axioms. It is these axioms that make some propositions of the logician school represented by Russell impossible in the strictest sense. ] use? We can apply the following theorem to define the addition of natural numbers. Theorem: Life "|N" means that * * * consists of all natural numbers, so we can uniquely define the mapping A: |NX |N→| N, so that it satisfies the following conditions: (1) For any element X in | n, we have a (x.

0)= x； (2) For any element X and Y in |N, we have a (X.

y*) = A(x

Y)*. Map A is the map we use to define addition. We can rewrite the above conditions as: (1) x+0 = x; (2) x+y* = (x+y)*. Now we can prove that "1+ 1 = 2" is as follows: 1+ 1 = 1 * (because1:. ] 1+ 1= 2 "can be said to be a" natural "conclusion drawn by human beings after introducing natural numbers and related operations. However, it was not until the19th century that mathematicians began to establish a strict logical foundation for the analysis based on real number system, and people really examined the basic problems about natural numbers. I believe that the most "classic" proof in this respect should be the one that appeared in "Principles of Mathematics" co-authored by Russell and Whitehead. We can prove "1+ 1 = 2": First, we can infer: α ε 1

y}。 & amp。 ~(x = y))ξε 1+ 1 & lt； = & gt(σx)(σy)(β= { x } ∨{ y }。 & amp。 ~(x=y)) So for any * * * γ, we have γ ε 1+ 1

y}。 & amp。 ~(x = y))& lt； = & gtγε2 According to zermelo-fraenkel of * * * theory, we get 1+ 1 = 2. ]

Reference: Yahoo

[email protected] @ I listened too deeply.

Prove that it is really the first time to meet you.

Picture reference:. Yimg/I/icon/16/31+1= 2, just like: picture reference: Ye * * * agazine/images/yes card /63/s/45 1 yes card = 2+. Because of this, the price will go up.

This is a mistake. Use more metaphors: picture reference: th133. photobucket/albums/q75/kseena/th _ dollar = picture reference: th133. photobucket/albums/q75/kseena/th _ dollar/kloc. Yuan+1 yuan = another metaphor of 2 yuan: picture reference: th206.photobucket/albums/bb52/cutii99/th_hand = picture reference: th206.photobucket/albums/bb52/cutii99/th_hand1hand+1 hand =2 hands. If =3 hands, are we 3-handed freaks? Picture reference:. yimg/i/icon/ 16/ 10

Reference: Me and photobucket

The people above copied it around.

I'm worried. A 5-point [ultimate math problem]

It's really hard. All right.

Let me give you a simple example. I am alone+looking at myself in the mirror = two me. Is that clear? Same as the unit (unit)

You can add it to the rack! This is the essence of 1+ 1 = 2! Where's the clock? Try adding 2+2.

Use different units

O plus what?

Reference: I use MS Excel+MS Access to count racks.

Why is 1+ 1 equal to 2? The university will have a certificate. A single certificate can make you copy softly. Don't underestimate this formula. 1+ 1=2 is one of the' greatest formulas' in science. Many people may ask, "Why 1+ 1=2?" This seems to be redundant (! ? ) problem. Now I'm trying to briefly introduce to interested netizens how to prove the mathematical statement "1+ 1=2" within the framework of axiomatic theory, which is "irrefutable" for most people. First of all, we should know that in the context of * * * theory, the objects we are discussing are all kinds of * * * (or classes, and the difference between them and * * * is not superfluous here), so the natural numbers we often encounter are also defined by * * * (or classes) here. For example, we can define 0, 1 and 2 (for example, qv. Quine) in the following way.

mathematical logic

Revised edition.

Chestnut 6

43-44):0:= { x:x = { y:~(y = y)} } 1:= { x:y(yεx . & amp； . x { y }ε0)} 2:= { x:y(yεx . & amp； . X {y} ε 1)} [For example, if we take an element from a molecule belonging to 1, then this molecule will become zero. In other words, 1 is a class composed of all classes with only one element. Now we generally use the method mainly introduced by von Neumann to define natural numbers. For example: 0: = λ

1:= {Λ} = {0} =0∪{0}

2:= {Λ

{Λ}} = {0

1} =1∨ {1} [λ is an empty set] Generally speaking, if we have constructed the set n,

Then its successor n * is defined as n ∨{ n}. In the general axiom system of * * * (such as ZFC), there is an axiom to ensure that this construction process can continue continuously, and all * * * obtained by this construction method can form a * * *, which is the so-called infinite axiom (of course, we assume that other axioms (such as the union axiom) have been established. Note: Infinite axioms are some so-called illogical axioms. It is these axioms that make some propositions of the logician school represented by Russell impossible in the strictest sense. ] use? We can apply the following theorem to define the addition of natural numbers. Theorem: Life "|N" means that * * * consists of all natural numbers, so we can uniquely define the mapping A: |NX |N→| N, so that it satisfies the following conditions: (1) For any element X in | n, we have a (x.

0)= x； (2) For any element X and Y in |N, we have a (X.

y*) = A(x

Y)*. Map A is the map we use to define addition. We can rewrite the above conditions as: (1) x+0 = x; (2) x+y* = (x+y)*. Now we can prove that "1+ 1 = 2" is as follows: 1+ 1 = 1 * (because1:. ] 1+ 1= 2 "can be said to be a" natural "conclusion drawn by human beings after introducing natural numbers and related operations. However, it was not until the19th century that mathematicians began to establish a strict logical foundation for the analysis based on real number system, and people really examined the basic problems about natural numbers. I believe that the most "classic" proof in this respect should be the one that appeared in "Principles of Mathematics" co-authored by Russell and Whitehead. We can prove "1+ 1 = 2": First, we can infer: α ε 1

y}。 & amp。 ~(x = y))ξε 1+ 1 & lt； = & gt(σx)(σy)(β= { x } ∨{ y }。 & amp。 ~(x=y)) So for any * * * γ, we have γ ε 1+ 1

y}。 & amp。 ~(x = y))& lt； = & gtγε2 According to zermelo-fraenkel of * * * theory, we get 1+ 1 = 2. Michael.

I have a cake.

Xiaoming gave me a cake.

As a result, I have two cakes. 2008-02-1321:48: 24 supplement:1= 2 2008-02-1321:49: 38 supplement:

Reference: I

Although I know it will slow down the passing rate, I still can't help but answer: If you can prove 1+ 1 = 2, everyone who knows the proof will definitely win the Fields Prize in mathematics, and it will take so much time to get your knowledge score. Tell me if what I said makes sense. 2008-02- 13 20:33:24 Supplement: Oh! There is not even a score of 10. The original score is only 5: 2008-02-13 20: 34: 51supplement: people who can prove that 1+ 1 = 2 will definitely shake the world, don't you think?

Although I don't know how to prove it, I can tell you some relevant knowledge. This is a topic of pure mathematics, which involves the nature of mathematics itself. To prove 1+ 1=2, we must first understand what 1 and 2 are, and we also need to know what 0 is. As for why we need to know what 0 is, it is because although 0 is an unrealistic number, it represents the abstract concept of numbers, and lets us know that numbers have their own value. Even if 0 does not exist, it has no size on the surface, but it plays a very important role in mathematics. In addition,+and = also appear in this formula, which is also indispensable. To prove 1+ 1=2 in detail, we must also understand the meaning of+and =. I hope this information can help you.

An apple+an apple =2 apples-> So 1+ 1=2.

1 plus 1 means 2 fingers instead of 3 fingers. ......

Reference: self

Why 1+ 1=2 Because of the wisdom left by our ancestors, if the knowledge left by our ancestors is 1+ 1=500, we must think that 1+ 1=2 ... Then our current cognition will become/kloc.