Unlike many significant mathematical proofs, such as the proof of the twin prime conjecture, incomplete and undecidable proofs are actually quite simple.

Many of the disciples of the Ten Thousand Methods Sect who participated in this training have already undergone many baptisms of the Three Views, and they have long had a trace of doubt in their hearts about the completeness, consistency, and decidability of arithmetic.

Now, in addition to the long-term subjective experience, there are also interpretations from the classics.

Most of those "classics" were written by the master.

Feng Luoyi, who was also a representative of the Geting School at the time, gave the final blow of "completeness", and the obstacles in everyone's perception began to shatter.

And the proof of indecidability was also taught to them

Feng Luoyi finally said to everyone: "Now, we have only published the first stage of the paper, "The Formally Undecidable Statements and Related Systems in the Arithmetic Chapter of Paper 1". The people only know the loss of completeness. Some monks don't even know anything about it.

Soon, we will publish the second phase of the paper, "On Computable Numbers and Their Application to Decision Theorems". That would have an even bigger impact.

Now, you have to give full play to the results of your training in the past few months, and use some methods to gently tell you the disciples of the Ten Thousand Fa Sect that the completeness and decidability have become history. That is your task now. ”

"Go ahead!"

In a short period of time, the many monks in the entire training ground were scattered like stars. Only a handful of people such as Chen Youjia are walking out slowly.

Chen Youjia was still hesitating, repeating in his heart: "Do you want to send a message to that guy to ask...... This time it had the greatest impact on the separation. He is a great master in the field of number theory, and he tends to deviate from the sect...... But. He's the current master of the Wanfa Gate, he must already know it...... He doesn't need me to care......"

"Yo!" suddenly. She was tapped on the shoulder...... Not. According to the sense of spiritual consciousness, it is a spirit being.

Chen Youjia turned around and saw Wang Qi's smiling face.

"Sure enough, it's you. Chen Youjia took a deep breath: "This time, it's all your fault, right? Although Mr. Feng didn't directly mention the author of the paper, I know that it's you ......."

Wang Qi pulled Chen Youjia to a secluded place...... While laughing: "Of course, apart from me, who can make such a huge breakthrough?"

Chen Youjia really wanted to sneer like before. But for some reason, she didn't say it.

Wang Qi's paper alone requires Xianmeng to spend half a year preparing and accepting.

He is not a genius, who dares to call it a genius?

Chen Youjia pouted: "Why did you think of coming to see me?"

"My broken paper is too lethal!" Wang Qi rubbed Chen Youjia's face unscrupulously: "Let's see if you are injured." ”

"Don't make a fuss. Chen Youjia waved away Wang Qi's hand: "You know, I am an arithmetic who is biased towards application, except for the element of anger, I actually don't take the dispute of leaving the sect so seriously. I don't care about that 'foundation'. Besides...... You also made the story of "Blade Assassin", right?"

Wang Qi immediately made a look of emotion: "I didn't expect that we already had a heart to this point! Come! Hug one!"

Chen Youjia was hugged by him. But he sneered: "Don't come, I have a good memory - then again, you told me a story a long time ago, why are you still worried that I won't accept it?"

"I have confidence in you, but let's take a look!" Wang Qi took two steps back: "Oh, I still have something to do over there, I have to go first!"

Looking at the vanished Wang Qi, Chen Youjia blinked, and then sent a spiritual message to his father: "How are you?"

There are only four words of hard bangbang.

Chen had not expected a response. Unexpectedly, her calculator immediately gave a prompt: "Peace." ”

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The corners of Wang Qi's mouth hooked into a smile. He was distracted and went to see Chen Youjia together. The projection of that "Wang Qi" is not only his distraction, but also synchronized with him through the illusion of ten thousand immortals.

"Do you have an idea again?" asked Turing Zhenren, who was sitting opposite Wang Qi.

Wang Qi shook his head: "No, no, I think of some other things." I'm still working on this idea of 'changing the sky'......"

"The limit of the sky-changing style...... Turing real person also felt a little heavy: "Xiangri, what we said about 'the changer who contains the sky in the formula' is the sky-changing style, and I think that the sky-changing style can be counted as everything...... I can't imagine that my algorithm, which can really do everything, can provide a way of thinking beyond the contradictions? ”

Since yesterday, the two of them have been discussing in one place. Wang Qi did not memorize too many papers in his previous life, and all the process of proof was deduced by him independently. Communicating with this genius has also benefited him a lot.

And Wang Qi also found that although the Turing real person spoke straighter and duller, he was still very good at talking. Occasionally, when he had a break, he would ask Turing for advice on some cultivation issues.

Ji Lao is the ancestor of the calculator, and he also appreciates Wang Qi's data-based cultivation method. And this ancestor of the calculator also gave Wang Qi a new understanding of the cultivation method.

The more they talked, the more speculative they became.

At this moment, they received a summons from Feng Luoyi. Then, the vision changed, and the two of them had already come to Feng Luoyi.

Feng Luoyi was gloomy and said, "Wang Qi, after seven days, I will arrange for you to give a public sermon, through the Ten Thousand Immortal Illusion Realm, to talk about this incomplete way for the entire Ten Thousand Methods." In the whole world, anyone can freely choose to listen or not to listen. You are well prepared. ”

After saying this, his expression was gloomy: "After all, I have to part ways with my old friend." ”

He is not an orthodox Geting faction, but he is also a representative of Geting. He has now made up his mind to support Wang Qi, and the promotion is undecidable and incomplete. This is in the opinion of the people of the Goting faction. It was he who gave the master a blow in the back.

This is undoubtedly a betrayal.

Turing Zhenren was relieved: "Brother Yuehan doesn't have to be like this. Lord Hemon was extraordinary. He Waier and He Daoyou are his descendants. He favored the queen of Lianzong, and the lord did not cut off contact with him, let alone you? You are now on the right side. ”

Wang Qi asked, "Teacher, what's going on with Lord Ximen?"

"Geting sent other Taoist friends to take care of it. Feng Luoyi sighed: "I hope I can survive this catastrophe." ”

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In the song garden, the fragrance is lingering. However, this finest spice can't hide the strong smell of gunpowder here.

"It's ridiculous!" a disciple of the Geting Sect scolded in a low voice.

They didn't dare to raise their voices too loudly, and even used their mana to concentrate their voices around them. I'm afraid of disturbing my teacher.

Now I don't know if the arithmetic master has read the paper "Formally Undecidable Statements and Related Systems in the Arithmetic Essay of Paper 1". They were now discussing how to stabilize their teachers.

"Why don't you do it......" One of the Goting monks sniffed and seemed to cry: "We tell the teacher, and we say that we still have a ...... to decidability."

"Don't!" Fairy Ruoche exclaimed in a low voice. Decidability will be rejected in a few days! Using this as a consolation is also looking for death!

And Ikeman took out another few pages: "This is the part that has not been released for the time being." ”

"What is this...... "On Computable Numbers and Their Applications to Decision Theorems" ......" The monk who read the paper was like being bombarded by great powers, and he was stunned.

――Is even the decidability finished?

――Some...... There are some propositions that we simply cannot determine whether they are true or false?

It's horrible......

Many of the high-ranking monks shuddered.

At this moment, the door of the inner room of the study was pushed open. The reckoning lord walked out with a confused expression.

"You ...... What are you doing here?"

"Teacher......" "Master!" "Teacher!" "Teacher!" everyone shouted in unison, and finally, Fairy Ruoche walked out. He asked, "Teacher, among the twenty-three questions." The second question has already been answered......"

"I know. The teller blinked. At this moment, he seemed to be an old man with memory loss, and his face was full of confusion: "I just read the paper...... I will be the first to know about the papers of the 23 questions. ”

Everyone breathed for a while.

He Waier came out of the crowd and said with concern: "Teacher, are you ...... now How are you now?"

"I'm fine. The reckoner replied, and then, as if to emphasize, repeated, "I'm fine." Although I didn't think about it...... I didn't expect the result to come out in such a form, but...... The second question has been made, and I am glad to congratulate you. ”

There was no trace of joy on his face.

"Teacher......" Ma Deen grabbed it: "If you are not happy...... You name it. ”

"There's no time to spare. The master finally smiled: "There is no time to complain." Don't we have something to do?"

Everyone was puzzled.

The main organization of the crowd gathered here for the purpose of proof of completeness, decidability, and consistency. Now, consistency has been proven, and decidability and completeness have been denied. What is Hepcher going to do?

"I'm thinking...... There may be something wrong with their thinking. Of course, there may not be any problem with the incompleteness itself, but can't it really be bypassed? After all, as an arithmetic proof, Wang Qi's incompleteness is too weak......"

The more the lord speaks, the more spirited he becomes. For a moment, Xi Baiche reappeared in the demeanor of the lord of the world's arithmetic gates.

However, He Waierzhi felt cold.

――Is this really self-confidence and new thinking?

――Or is it a form of self-deception and self-comfort?

Ruoche, Ikeman, Ma Deen and other carefree monks were full of sadness in their hearts.

They feel that they have witnessed the twilight of a generation of talents and heroes.

Although in terms of age, the teacher is still a young man. The years he spent were short compared to the life span he still had. But the way of the Lord Hepache is dead.

-- In this turmoil, almost no one in the Ten Thousand Laws Gate has been able to take the opportunity to reach the top. (To be continued.) )

PS: The twilight of heroes is always the most impressive.

In addition, the alliance leader adds five more, and the big alliance ten is more effective for a long time. He Meng's main addition will be released on a later date next week.