Enter the Immortal Cultivation

For mathematicians on Earth, a mental breakdown caused by a certain theorem is at most a madness. The number of mathematicians who have been in mental hospitals is only less than that of writers who have been in mental hospitals.

For the monks in Shenzhou, if their Taoism is broken, it may lead to physical death.

Therefore, Gödel's incompleteness theorem is very dangerous for the monks in Shenzhou.

Even for people like Wang Qi who knew this theorem in his previous life and then derived it personally in this life, they are in danger.

However, Wang Qi knows that this should not be a life-threatening situation.

By the way, just in case, he has estimated ten possible states in advance and made twelve contingency plans.

Among them, "condition B" refers to his current state.

The collapse did happen, it was very serious, and no means could contain it. However, at the last moment, the collapse will stop automatically, leaving Wang Qi a ray of life.

The view that "all axiom systems are incomplete" is just a misunderstanding of Gödel's incompleteness theorem by ordinary people. In fact, complete systems known to humans do exist. Take Euclidean geometry, for example. It can be axiomatized into a complete system. In addition, Gödel's completeness theorem [in Shenzhou, it is called 'Wang's completeness law'] proposed by Wang Qi several years ago also explains the completeness of all first-order logic systems.

Collapse is not endless. At least in Wang Qi's revision method, there are still things that cannot be doubted or overturned even if they are "incomplete".

Wang Qi felt his condition. He only had a ray of life left. He was dying. However, the pen in his hand had not stopped.

Because he had made preparations and left a backup.

The ring "Mathematics" on Wang Qi's hand and the shoulder armor "Discrete" on his shoulder lit up one by one, and then Jarvis input a new spell into Wang Qi's body.

——"Because it is incomplete. We can never prove that an axiomatic system is free of contradictions", which is also a misunderstanding of Gödel's incompleteness theorem.

Gödel's incompleteness theorem denies the possibility of "proving the consistency of a system within a system". This proof process is complicated to explain, but its core idea is to use the so-called "self-reference".

——This statement states itself.

——This set includes itself.

This is also the source of many paradoxes in logic. The "barber paradox" on Earth and the "alchemist paradox" in China are ultimately caused by the question of "whether a set should include itself".

And this incompleteness law can be bypassed.

The completeness of the system cannot be proved within the system. But it can be proved from outside the system.

We cannot prove the system based on the system itself. But we can prove it through another system.

Wang Qi did relevant theoretical research five or six years ago.

It is the idea of ​​the Bourbaki school!

Prove it from the outside!

The Bourbaki school is something that the mathematics community on Earth has re-derived after being severely washed by Gödel's incompleteness theorem. If it is classified according to China, it also belongs to the Lizong line. The method of revision deduced according to the theory of the Bourbaki school can also support the mana system that collapsed due to the incompleteness law.

The support given by Jarvis is re-directing the mana that collapsed in Wang Qi's body.

At the same time. Wang Qi's paper is also nearing the end.

"Conclusion... From this, I can prove that for any mathematical system, if it contains an arithmetic system, then this system cannot satisfy completeness and consistency at the same time. For any arithmetic system, if it contains an arithmetic system, then we cannot prove its consistency within this system..."

-Completeness and consistency cannot be achieved at the same time. This system is either self-contradictory or there are propositions that can neither be proved nor disproved!

Boom!

Wang Qi's mind was like a flash of lightning. He felt refreshed and had never been so clear-headed.

On the other hand. His mana system collapsed and reunited, which was almost equivalent to experiencing a nirvana. His cultivation is still in the early stage of Jindan, but the essence of the method of revision is sublimated.

Pah pah pah pah pah…

A series of crisp sounds came from the air, like a torn cloth. That was the disturbance of the surroundings caused by Wang Qi's unconscious mana.

He stood up, then sat down again and thought about it. He picked up a piece of paper again and wrote an appendix. He reiterated the nature of Gödel's incompleteness theorem and attached the papers he had been working on intermittently in recent years on "transfinite induction" and "arithmetic axiomatization".

Even he himself encountered a major collapse of the law when writing this paper. What would happen if it was someone else?

Therefore, some "safety measures" must be added.

Although Gödel's incompleteness theorem occupies an extremely important position in the history of mathematics, the proof process is relatively simple and the paper as a whole is very short. With Wang Qi's thinking speed and hand speed, the whole paper was written in an hour or so.

He pushed the door open and Chen Youjia suddenly rushed over, grabbed his collar, and scolded: "What the hell are you doing?"

"Writing a paper..."

"You almost died..." Chen Youjia's originally indifferent expression became very obvious at this moment, and anger and grievance appeared in her eyes at the same time. She used her magic power to restrain the tears overflowing from the corners of her eyes, gnashing her teeth and saying: "You almost died... You almost died! What kind of paper are you writing?"

Only then did Wang Qi remember that he only sealed the doors and windows and forgot to block the breath.

"Back then, Senior Pu who pioneered the Misty Way ran out of power because he discovered discontinuity." Wang Qi patted Chen Youjia on the shoulder: "Same truth..."

Chen Youjia took a breath, then calmed down: "Really..." She buried her head on Wang Qi's shoulder: "Is that so..."

If someone else said that he was going to subvert the existing academic system, Chen Youjia would probably think that he was crazy or essentially uneducated. But for some reason, when Wang Qi said this, she believed it.

It's strange that although Wang Qi was brilliant in the past, he was limited to the category of "genius". It is not credible to say that he can produce results of Xiaoyao series now. However, Chen Youjia believed it.

Although Wang Qi is crazy, he has never been crazy in this matter.

"Hey, junior brother." Mi suddenly appeared and said to Wang Qi, "Master is looking for you."

"Huh?" Wang Qi was a little surprised. Chen Youjia asked doubtfully: "Is Mr. Feng looking for you? Is it the paper you just wrote?"

"Absolutely not." Wang Qi still understood the importance. Before writing his thesis, he installed several firewalls on his calculator to prevent Feng Luoyi from seeing it. Moreover, he also used magic power to spread around, and the digital cultivation method was also the nemesis of the calculator's simulated spiritual consciousness. There is no way Feng Luoyi knew all this.

If I have to say... maybe... maybe it's because of some of the "ideas" he expressed before?

Wang Qi was a little confused. He quickly completed the thesis with his calculator ring, then put the manuscript paper in his hand into his storage bag, sealing it with force to ensure that it would not be opened by anyone.

Chen Youjia is here. It's really dangerous for her to see.

With a little pressure and excitement, Wang Qi once again dived into the fantasy world of ten thousand immortals.

Feng Luoyi had long been waiting for Wang Qi in a fantasy world. This still looks like a library. Feng Luoyi and Wang Qi sat opposite each other. With a hint of anger on his face, the old man scolded: "Wang Qi... what have you been thinking about recently?"

"I have recently been trying to describe arithmetic in straightforward language. This process does not involve too complex arithmetic principles, so it is very suitable for promotion." Wang Qi said respectfully: "I plan to print it into The book will be promoted throughout the world to spread my teachings, so that everyone in the world can know the principles of my teachings and let more people join in. "

Popularizing science is also a good way to gain reputation.

Hawking is the best example. This is also one of Wang Qi's plans, but it is just a long-term plan.

Feng Luoyi accepted Wang Qi's statement, but snorted coldly: "It's good that you have this intention. But don't you think that some of the 'principles' you want to promote are really too presumptuous?"

Wang Qi pretended to be confused and said, "Teacher, what do you think?"

"'Numbers themselves are things in themselves that transcend our thinking', 'Logically we cannot deny the possibility that one plus one equals three', 'No one worries about the problem that one plus one equals three'." Feng Luoyi glared at Wang Qi : "What do you want to say? You don't mean that everyone relies on a sense of super logic to complete the initial accumulation of arithmetic, right?"

"I just demonstrated the possibility." Wang Qi still maintained a low profile: "Actually, before the master has proved the completeness of set theory, we can only say 'it is possible'. We really cannot deny the proof from a logical level The possibility of 'one plus one equals three'. As for the other two, I'm just stating the facts."

Feng Luoyi was helpless: "When did you fall in love with Suanjun's Lian Zong?"

"This disciple has never been biased towards Lian Zong, who is the king." Wang Qi said respectfully. Perhaps in terms of "completeness", Li Zong's thought failed miserably, but Li Zong's research ideas and working methods are both advisable. At least that's what Wang Qi thinks.

"But your idea is already a bit dangerous."

Wang Qi said respectfully: "Because from my perspective, the existing logic is really unreliable."

"Unreliable?" Feng Luoyi smiled. Wang Qi felt that a large amount of offensive data flow was almost overwhelming him.

"Tell me, why are you unreliable? What's so unreliable?"

“Can you find anything in the existing system that it cannot explain?”

Wang Qi said: "It's just existing."

"Can you still see what is not there now? Did you create a new branch of arithmetic yourself and then prove that it cannot be axiomatized?"

"No, teacher." Wang Qi shook his head: "I did not create a branch, but calculated the future." (To be continued ~^~)

PS: I will be pretending to be a **** in the next few days. Please give me monthly tickets, please give me monthly tickets, and also recommend tickets.