Enter the Immortal Cultivation

"Arithmetic... is incomplete?" After hearing this, Bo Xiaoya's first reaction was - are you kidding me?

Is the learning incomplete?

How can arithmetic be incomplete?

Arithmetic must be complete!

Even those who are completely different from the master in arithmetic concepts agree with his famous saying, "We will know, we must know."

For the calculator and his followers, arithmetic must be complete and consistent. In the eyes of these monks, the ontology of arithmetic is the "form" composed of operators. Every statement composed of operators can be judged as "correct" or "wrong", and a correct statement can definitely be proved by another combination of operators. In addition, a statement can always only be judged as "correct" or "wrong". There is no such thing as "both right and wrong" or "neither right nor wrong".

Completeness, consistency, and decidability are the foundation of Suzhu and the beliefs of the Geting School.

For ordinary mathematicians, although this part is inevitable, they intuitively feel that the math must be complete.

Those monks who are studying the laws of material flow have been surprised to find countless times that when they are thinking about launching an attack in a certain field, the mathematicians of Wanfa Sect have already prepared the "tool for seeking the truth" for them - arithmetic. formula. From the earliest Yuanli Sect, to Guiyi League, and now to today's Piaomiao Palace, these sects that explore the world through empirical research have been providing more and more formulas to Wanfa Sect - derived from all things in the world and Tao following nature. An exquisite formula. These formulas fed back the development of arithmetic.

In the view of the monks of Wanfamen. Everything in the universe moves respectfully according to the laws of arithmetic.

When you say that arithmetic is incomplete, are you saying that there is something wrong with the world and the way of heaven?

Bo Xiaofeng is more stable than his sister. He held Su Junyu's shoulders. After passing through a stream of inner energy, he said: "Su Junyu, stabilize your mind and guard against the breeding of inner demons..."

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

Su Junyu smiled, waved away Bo Xiaofeng's hand, and saluted the Yuanshen Grandmaster. He said: "My disciple is very good. I'm sorry for bothering you, uncle."

After leaving all the monks from Yangshen Pavilion, Su Junyu said with burning eyes, "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 Li Zong." Suo Wenhong frowned in disgust: "This is just... just..."

For Lian Zong disciples, some things are self-evident and cannot be denied.

For the disciples of Li Zong. Some things are inevitable, but they have not been proven and cannot be denied.

Only on this point, Li Zong and Lian Zong held the same views.

Qin Chuanhe also frowned: "Where's the proof?"

Su Junyu shrugged: "Not yet, not yet."

"Not yet, how dare you say such a thing..."

"It's not a formal occasion anyway." Su Junyu didn't care.

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

"I'm thinking that this study must be to pave the way or buffer the new theory. However, what we are studying now are all some 'axiomatic' or 'axiom system completeness proofs'. Not to mention a few of these things A hundred years ago, just a few years ago, there was another breakthrough. This is definitely not something subversive." Su Junyu said slowly: "Since what we are learning is not the subversive content itself, That must be the precursor to the subversive content, or something that can offset the impact of the subversive content.”

Bo Xiaofeng nodded. He said that what Su Junyu said was reasonable.

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

"And have you noticed that the things we have learned have a characteristic - they are all the product of 'a certain thought', and they are all tricks used to bypass 'a certain high wall'."

Bo Xiaoya reacted immediately: "The idea that Senior Brother Wang Qi mentioned seven years ago... this trick is to... to bypass the proof of multi-level logical completeness!"

——This Wang Qi again...

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

"If the completeness is proven, then none of these things have any meaning!" Su Junyu retorted: "And the calculation is complete and does not contradict any of us' intuitive feelings! That is not considered 'subversion'!"

Suo Wenhong shook his head: "It's unreasonable."

Qin Chuanhe roared: "Prove! You must provide proof for this idea!"

By the end of the conversation, almost everyone left with anger. Su Junyu's brows furrowed deeply again.

Yes...proof, proof must be given...

——But, Wang Qi, if you really made such an incredible achievement, how did you prove it?

For the first time, Su Junyu felt a little powerless. He thought about the important truth of "incompleteness". Or it was inspired by the truth in Wang Qi's notes that "even the simplest numbers have meanings beyond human thinking." Let him figure out the proof independently...

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

"Blade Assassin", "self-referential".

In the end, Su Junyu also sighed deeply.

——Damn, I can’t catch up with that kid’s train of thought.

………………………………………………………………………………………………………………………………

In the fantasy world of Ten Thousand Immortals, Fairy Feng Luoyi and Ruo Che watched the whole scene.

There was a sarcasm in Fairy Ruoche's tone, and she was very bitter: "It seems that your and Wang Qi's hard work was in vain. No one realized that the mirage play was the answer to this puzzle. The key...self-referring, self-referring...hehehe."

Feng Luoyi's tone was calm: "It's a good sign after all."

Fairy Ruoche said: "What should we do next? Should we use a more explicit prompt?"

Feng Luoyi shook his head: "It's not necessary for the time being. The most important thing for us is to guide and observe the changes in these people's thinking processes." He paused, and then said: "Observe for another seven days. If this suspicion has not been ignored or forgotten, If there are any signs, then let the first batch of Yuanshen monks join this training session.”

Fairy Ruoche smiled bitterly: "Looking at them one by one, they have obviously mastered the most critical key but can't get in, I seem to see myself... I have been like a headless fly for hundreds of years, not knowing anything. , running around, but not knowing that Baoshan is around. Haha, what an ancient theory. Self-referring..."

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

"When most people think about this problem, they will only fall into the maze of layers of self and find it difficult to extricate themselves. However, there is a kind of genius who is able to cut through the layers of illusion and see the core thing." Feng Luoyi said calmly.

The proof of Gödel's incompleteness theorem-Wang's incompleteness law was not achieved overnight. It also requires tortuous and difficult thinking.

"Is Wang Qi that genius?"

"He is undoubtedly a genius." Seeing that Fairy Ruoche was not very interested, Feng Luoyi changed the subject: "Speaking of which, how is Master Ximen doing?"

"Master's side..." Fairy Ruoche smiled bitterly: "It's probably because the barriers to knowledge and vision are too terrible. He is not aware of this problem at all. And... and..."

Feng Luoyi frowned: "And what? Are there any other problems?"

"Actually, there is a thought that has emerged within the Geting sect." Fairy Ruoche was a little embarrassed to speak: "They said that the expression and proof of incomplete laws are too arbitrary. The concept of 'incomplete arithmetic' was put into words There are only four short words, but they can hardly be expressed using arithmetic. They feel that as long as they refuse to admit that this is arithmetic and regard it as a 'word game' in their hearts, they can... avoid the Taoist mind. shake."

"Haha." Feng Luoyi's face showed a sarcastic look: "This is how you despised us, and now we still use this way to despise others?"

Fairy Ruoche sighed: "But... it is indeed not a mathematical statement... Perhaps, this idea can be used to protect the teacher..."

Feng Luoyi said angrily: "Do you want Master Ximen to be that cowardly person?"

Fairy Ruoche sighed: "It's not a complete law, and the persuasiveness is still a bit lacking."

…………………………………………………………………………………………………………

"It seems that the persuasive power of incomplete laws does have some shortcomings..."

This is what Wang Qi came up with after sending spiritual messages to Chen Youjia for the seventh time without success.

Gödel's incomplete laws have shown extraordinary value in the field of earth philosophy. Together with the unfathomable principle of quantum mechanics, it forms the basis of human cognitive concepts in the new century. But relatively, its mathematical significance is not that great. It is a milestone in mathematics, but its shadow is rarely seen in subsequent fields.

Because, in the eyes of practical people, Gödel's incompleteness law is meaningless. In the eyes of those who prefer theory, Gödel's incomplete laws are not mathematical enough.

"Should I add more fire..."

As long as I add more fire, the teacher's resistance to promoting this theorem may be much smaller... Yujia no longer has to stay in Wanfamen, so... my plan can also be implemented faster...

Wang Qi's thoughts gradually turned to this aspect.

If we want to talk about irrefutable persuasion...

"Shall I solve the first of Ximen's twenty-three questions?"

Wang Qi happens to know how to increase the persuasiveness of his own theoretical system. (To be continued ~^~)