For the mathematicians of the earth, to be mentally broken by a certain theorem is, at best, to go crazy. The number of mathematicians who have spent time in mental hospitals is only less than that of literary scholars who have spent time in mental hospitals.

For the monks of Shenzhou, if the Dao Heart is broken, it may bring about physical death.

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

Even for people like Wang Qi, who knew this theorem in his previous life, and then deduced it himself in this life, he is in danger.

However, Wang Qi knew that this should not be life-threatening.

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

"Condition B" refers to his present state.

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

The idea that "all axiomatic systems are incomplete" is just a misreading of Gödel's law of incompleteness. In fact, there are complete systems known to man. Euclidean geometry, for example, can be axiomatized as a complete system. In addition, the Gödel completeness theorem [in Shenzhou, it is called Wang's completeness law"] thrown out by Wang Qi a few years ago also illustrates the completeness of all first-order logical systems.

The collapse is not endless. At least in Wang Qi's cultivation, there are still things that are "incomplete" and cannot be doubted or subverted.

Wang Qi sensed his condition. There was only one line left in his life, and his life was in danger. However, the pen in his hand has not stopped.

Because he was ready, he left behind.

The ring "mathematics" on Wang Qi's hand. The shoulder armor on the shoulder "discrete" lit up in turn. And then. Jarvis fed a new recipe into Wang's body.

- "We can never prove that an axiomatic system is free of contradictions because it is incomplete" is also a misreading of Gödel's incompleteness theorem.

Gödel's incompleteness theorem rejects the possibility of "proving the consistency of a system within the system", which is a complex process to prove, but the core idea is the use of the so-called "self-referential".

- This statement states itself.

- This collection contains itself.

This is also the source of many paradoxes in logic. The "barber paradox" of the earth and the "alchemist paradox" of China are, in the final analysis, caused by the question of "whether a collection should include itself".

And this law of incompleteness can be bypassed.

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

We can't prove this system by the system itself, but we can prove it by another system.

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

Exactly, the ideas of the Bourbaki school!

Prove from the outside!

The Bourbaki school is something that has been re-derived from the earth's mathematical community after being severely washed by Gödel's incompleteness theorem. If it is according to the classification of Shenzhou, it also belongs to the lineage of separation. And the cultivation method deduced according to the theory of the Bourbaki school is also able to support the mana system that has collapsed due to incomplete laws.

The support given by Jarvis is redirecting the disintegrating mana in Wang Qi's body.

At the same time, Wang Qi's thesis was also nearing its end.

"Conclusion...... From this, I can attest to it. For any arithmetic system, if it contains an arithmetic system. Then the system cannot meet both completeness and consistency. For any arithmetic system, if it contains an arithmetic system, then we cannot prove its consistency within the system......"

- Completeness and consistency cannot be combined, and the system is either self-contradictory or has propositions that can neither be proved nor falsified!

Bang!

There was a thunderbolt in Wang Qi's mind. He felt refreshed, he had never been so awake before.

On the other hand, his mana system disintegrated and reunited, almost equivalent to experiencing a nirvana. His cultivation is still in the early stage of the Yudan, but the essence of his cultivation is implicitly sublimated.

Bang Bang ......

There was a series of crunching sounds in the air, like cracks. It was Wang Qi's unconscious mana that was disturbing the surroundings.

He stood up, then sat down again, and thought for a moment. Picking up a piece of paper again, he wrote an appendix, again stating the nature of Gödel's law of incompleteness, and attaching the papers he had worked on and off over the past few years on "transcendent induction" and "axiomatization of arithmetic".

Even he himself, while writing this paper, suffered a great collapse in Fa cultivation, what would happen if it were someone else?

Therefore, there must be a little "insurance measure" attached.

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

He pushed the door out, and Chen Youjia suddenly pounced, grabbed him by the collar, and scolded, "What the hell are you doing?"

"Writing a Dissertation ......"

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

Wang Qi then remembered that he had just sealed the doors and windows and forgot to shield his breath.

"Back then, Pu's predecessors, who pioneered the ethereal way, lost their power because they discovered discontinuity. Wang Qi patted Chen Youjia on the shoulder: "It's almost the same ......"

Chen Youjia breathed for a moment, and then stabilized: "Is it......" Her head was buried in Wang Qi's shoulder: "That's it......"

If others say that they are going to subvert the existing academic system, then Chen Youjia will probably think that he is crazy, or that he is essentially uneducated. But for some reason, Wang Qi said so, and she believed it.

It is strange that although Wang Qi was brilliant in the past, it was limited to the category of "genius", and it is not very credible to say that he can make the results of the free series now. However, Chen Youjia just 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 wondered: "Could it be that Mr. Feng is looking for you? Is it the paper you just wrote?"

"Absolutely not. "Wang Qi still knows the severity. Before writing his thesis, he had placed several firewalls in his calculator to prevent Feng Luoyi's sight. Moreover, he also used mana to spread the surroundings, and the digital cultivation method is also the nemesis of the calculator simulation of spiritual sense. Feng Luoyi couldn't have known all of this at all.

If you have to say it...... Maybe...... Maybe it's because of some of the "thoughts" he showed before?

Wang Qi was a little puzzled. He quickly completed the fall of the paper with his calculator ring, and then put the manuscript paper in his hand into his storage bag, sealing it with a strong horizontal cultivation to ensure that it would not be opened by anyone.

Chen Youjia is here. Let her see, it's really dangerous.

With a little pressure and excitement, Wang Qi once again infiltrated the Ten Thousand Immortals Fantasy Realm.

Feng Luoyi had been waiting for Wang Qi in a fantasy world for a long time. It's still a library. Feng Luoyi and Wang Qi sat opposite each other. With a faint look of anger on his face, the old man scolded: "Wang Qi...... What have you been thinking lately?"

"I've been trying to put arithmetic in plain language lately. This process, because it does not involve too complicated arithmetic principles, is very suitable for promotion. Wang Qi said respectfully: "I am going to print it into a book and promote it throughout the world to spread the way of my ten thousand laws, in order to let everyone in the world know the truth of my ten thousand methods and let more people devote themselves to it." ”

Popular science is also a good way to gain fame.

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

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

Wang Qi pretended to be confused: "Teacher, what do you say?"

"'Numbers themselves are something that transcends our thinking', 'logically we cannot deny the possibility that one plus one equals three', 'no one worries about the question of one plus one equals three'. Feng Luoyi glared at Wang Qi: "What do you want to say? What do you mean, shouldn't you say that everyone relies on the feeling of super-logic to complete the initial accumulation of arithmetic?"

"I'm just arguing for the possibility. Wang Qi still kept a low profile: "In fact, before the master proves the completeness of set theory, we can only say 'possible'." We really can't logically deny the possibility of proving that 'one plus one equals three'. As for the other two, I'm just stating the facts. ”

Feng Luoyi was helpless: "When did you fall to Lian Zong, who is counting the monarch?"

"The disciple has never been biased towards the Lian Sect of the Counter. Wang Qi said respectfully. Perhaps in terms of "completeness," the idea of departing from the sect has failed completely, but the research ideas and working methods of the departing ideology are all desirable. At least that's what Wang Qi thinks.

"But your ideas are already in danger. ”

Wang Qi said respectfully: "Because from the disciple's point of view, the existing logic is really unreliable. ”

"Unreliable?" Feng Luoyi smiled. Wang Qi felt that a large amount of aggressive data streams were being used, almost overwhelming him.

"Tell me, why is it unreliable? What's unreliable?"

"Can you find something in the existing system that it can't explain?"

Wang Qi said: "It's just existing." ”

"Can you still see what you don't have now? Have you created a new branch of arithmetic yourself, and then proved that it cannot be axiomatized?"

"No, teacher. Wang Qi shook his head: "I didn't create a branch, but calculated the future." (To be continued.) )

PS: I'm going to install a **** in the next few days, ask for a monthly pass, ask for a monthly pass, and recommend a recommended ticket