Into the Immortal Cultivation

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"Study ... not perfect?" After hearing this sentence, Bo Xiaoya's first reaction was-why are you teasing me?

Is it incomplete?

How can mathematics be incomplete?

Math must be complete!

Even someone who is completely different from the operator in terms of arithmetic, agrees with his famous saying that "we must know, we must know".

For the master and his followers, mathematics must be complete and consistent. In the eyes of these monks, the ontology of mathematics is the "form" composed of operators. Every statement composed of operators can be judged as "correct" or "wrong". The correct statement must be proved by another combination of operators. In addition, a statement will always only have "correct" or "wrong" judgments. There can be no so-called "right and wrong" or "incorrect or wrong" situation.

Completeness, consistency, and decidability are the foundations of the fortunetellers and the beliefs of the Goettins.

For ordinary mathematicians, although this part is inevitable, they intuitively think that arithmetic must be complete.

Those monks who have exhausted the laws of the circulation of matter have discovered amazed countless times that when they are thinking of attacking in certain fields, the mathematicians of Wan Famen have already prepared for them the "approach for the way"-arithmetic Formula. From the earliest Yuanli Sect, to the Gui Yimeng, and now to the Nianji Temple, these schools of empirical exploration of heaven and earth have been providing more and more formulas to Wanfamen-derived from heaven and earth, everything Subtle formula. These formulas feed back the development of mathematics.

In the view of the monks of Ten Thousand Famen, everything in the universe moves along the law of arithmetic with respect and respect.

You said that the study is not complete, that is to say, there is a defect in this world, there is a problem in this heaven and earth?

Bo Xiaofeng is more stable than his sister. He held Su Junyu's shoulder and passed through the inner air: "Su Junyu, stabilize your mind and beware of the growth of mind demons ..."

On the other side, a guru of Yangshen Pavilion couldn't sit still and ran over and asked, "Do you need help?"

Su Junyu smiled, waved his hand with thin smile, and saluted the Master Yuanshen, saying, "The disciples are very good, and bother this Master."

After the monk in the Yangshen Pavilion was gone, Su Junyu's eyes were burning, and he said, "I'm not crazy, I'm just explaining a possibility."

"Possibility? You call this 'possibility'?" Bo Xiaofeng frowned: "Are you crazy? Is this possible?"

"Until the completeness is proven, no one can deny this possibility." Su Junyu said seriously: "We don't know from beginning to end ..."

"This is the result of believing in Lizong." Suo Wenhong frowned in disgust: "This is purely ... is ..."

For Lianzong disciples, there are certain things that are self-explanatory and cannot be denied.

For Lizong disciples, some things are inevitable, but they have not been proven and cannot be denied.

Only on this point, the views of Lizong and Lianzong have been the same.

Qin Chuanhe also frowned: "Proof?"

Su Junyu shrugged: "For now, not yet."

"Not yet, you dare to say this ..."

"It's not an official occasion anyway" Su Junyu doesn't matter.

Bo Xiaofeng was curious: "Su Junyu, what is your idea?"

"I'm thinking that this study must be for the purpose of paving or buffering new theories. However, what we are studying now is some 'axiomatization' or 'proof of the completeness of the axiomatic system.' A hundred years ago, just a few years ago, there was a new breakthrough. This is definitely not a subversive thing. "Su Junyu said slowly:" Since what we are learning is not the subversive content itself, That must be the front of the subversive content, or something that can offset the impact of the subversive content. "

Bo Xiaofeng nodded, indicating that Su Junyu's remarks were reasonable.

"Since that subversive theory must be related to what we have learned in the past few days, it is relatively simple to think from what we have learned in the past few days."

"And you noticed that there is a characteristic of what we have learned-they are all products of" a certain idea ", all of which are tricks to bypass" a certain high wall. "

Bo Xiaoya immediately reacted: "The thought that Brother Wang Qi said seven years ago ... This trick is for ... To prove the completeness of multi-level logic!"

——This is Wang Qi again ...

Qin Chuanhe frowned unconsciously: "What we have learned is a trick to bypass the multi-level logic completeness proof, so you guess that it is incomplete. Why don't you say that completeness has been proved? "

"If the completeness is proved, then these things have no meaning!" Su Junyu retorted: "And the completeness of learning is not inconsistent with any of us' intuitive feelings! It would not be considered 'subversion'!"

Suo Wenhong shook his head: "Unreasonable"

Qin Chuan He then shouted: "Prove! This idea, you must give proof!"

At the end of this conversation, almost everyone left with anger. Su Junyu frowned deeply again.

Yeah ... proof, proof must be given ...

——But, Wang Qi, if your kid really made such a remarkable achievement, how did you prove it?

For the first time, Su Junyu felt a little powerless. He thought about the important principle of "incompleteness". It's because he was inspired by Wang Qi's note that "even the simplest numbers have meanings beyond human thinking." Let him independently come up with proof methods ...

Due to cognitive reasons, Su Junyu did not realize that Wang Qi and Feng Luoyi had already given him the key hint of this proof.

"Silverwing Assassin", "self-referred."

In the end, Su Junyu also sighed deeply.

——Fuck, I ca n’t catch up with the kid ’s thoughts.

....................................................................................................................................

In the fairyland of Wan Xian, Feng Luoyi and Ruo Che Fairy watched this scene throughout.

If there was a sarcasm in the voice of Fairy Che, nine points bitter: "It seems that you and Wang Qi's pains are in vain. No one realizes that the trick is to solve this puzzle. The key ... self-referring, self-referring ... hehehe. "

Feng Luoyi said calmly: "After all, it is a good phenomenon."

Ruo Che fairy said: "What should I do next? Do you want to use more explicit tips?"

Feng Luoyi shook his head: "It is not necessary for the time being. The most important thing is to guide and observe the changes in the thinking process of these people." He paused and then said: "Observe for another seven days. If this doubt has not been ignored or forgotten Signs, let the first batch of Yuanshen monks join this training. "

Ruo Che fairy smiled bitterly: "Looking at them, one by one, has mastered the most critical key but can't get in, I feel as if I have seen myself ... For hundreds of years, it's like a headless fly, nothing is clear. , Messing around, without knowing Baoshan is by his side. The 'Alchemy Master Paradox', huh, what an old theory. Self-referring ... self-referring ... "

In the end, all the emotions turned into a sigh: "Why didn't I think of it?"

"Ordinary people think about this problem, they will only fall into the maze of layers of self, and it is difficult to extricate themselves. However, there is a genius, he can just cut through the vain and see the most core things." Feng Luoyi tone calm.

Gödel's incompleteness theorem, the proof of Wang's incomplete law, is not done overnight. It also requires tortuous and difficult thinking.

"Wang Qi is that genius?"

"He is undoubtedly a genius." Seeing that Ruo Che was not interested, Feng Luoyi changed the subject: "Having said, what happened to Lord Ximen?"

"Master's side ..." Ruo Che fairy smiled bitterly: "It's probably too terrible to see obstacles. He didn't realize the problem at all. And ... and ..."

Feng Luoyi frowned: "And what? Any questions?"

"Actually, there is also an idea within the Geting School." Fairy Ruoche was a little ashamed to say: "They said that the expression and proof of imperfect laws are too arbitrary. The concept of 'calculating incompletely' is put into text. There are only four short words, but they are almost impossible to express with an operator ... They feel that as long as they die, they do not admit that this is a mathematics, and they can treat it as a "word game" in their hearts ... shake."

"Oh." Feng Luoyi's face sneered: "Suanjun despised us in this way, and now we still have to despise others in this way?"

Ruo Che fairy sighed: "But ... it really is not a statement of mathematics ... maybe, this idea can be used to protect the teacher ..."

Feng Luoyi said angrily: "Do you want Master Ximen to be the kind of gutsless rat?"

Ruo Che fairy sighed: "Incomplete law, persuasion is still insufficient."

........................................................................................................................

"It seems that there is indeed some deficiency in the persuasion of incomplete laws ..."

This is what Wang Qi came up with after he failed to send a spiritual message to Chen Youjia for the seventh time.

Gödel's law of incompleteness has shown extraordinary value in the field of philosophy of the earth. Together with the unpredictable principle of quantum mechanics, it forms the basis of human cognitive concepts in the new century. But relatively, its significance in mathematics is not so great. It is a milestone in mathematics, but it is rarely seen in the field behind it.

Because, in the eyes of actual people, Gödel's incomplete law is meaningless. In the eyes of theory-biased people, Gödel's incomplete laws are not mathematical enough.

"Should I add another fire ..."

As long as I add another fire, the resistance of the teacher to promote this theorem will probably be much smaller ... Yujia does n’t need to stay in the same way ... my plan can be carried out more quickly ...

Wang Qi's mind gradually turned to this aspect.

If you want to say irrefutable persuasion ...

"Do I want to solve the first question of Ximen's twenty-three?"

Wang Qi happened to know how to increase the persuasive power of his theoretical system.

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