Vol 3 Chapter 2089: Strange phenomenon 【Chapter three】

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The undecidability of the semigroup word problem is the first human discovery that is not made by a mathematician, but a naturally existing undecidability problem.
It also means another truth.
"Undecidability is more than just being confined to pure arithmetic".
It seems to emphasize the objectivity of the concept of "undecidability".
Numerous monks of the Zongzong dynasty were convicted. They really cannot believe that the language that constitutes their thinking actually contains the danger of "undecidability".
However, for a while, they couldn't even find the reason for the rebuttal.
Because in the field of "linguistics", Wang Qi occupies a monopoly position, and he uses arithmetic and logic to deal with the problem of words.
This is undoubtedly a detached field.
Lianzong couldn't even find the point to show his fists and was unable to exert his strength.
"This ... Feng Luoyi, Wang Qi, this pair of mentors and disciples, are they going to work together to destroy the door?"
There was even a monk shouting in horror.
However, Lizong is also uncomfortable compared to Lianzong.
This paper, however, once again emphasizes the status of "undecidability".
"This guy, in order to promote himself, so take us to start?"
Some Lizong monks also gritted their teeth.
This paper by Wang Qi is undoubtedly a heavy punch, hitting the backbone of Lizong monk hard.
At this time, no matter whether it was Lizong or Lianzong, there was no benefit.
However, soon, Lian Zong Xiaoyao responded.
A number of Lianzong Xiaoyao has ended their current mission in Zhengshi Division and concentrated on preparing this debate.
Now, within Lianzong, new directions are gradually appearing.
They actually tried to learn the "logic" of the sect, absorbed the knowledge of the sect, and countered the sect with the theory of the sect.
This should be regarded as a counterattack to Feng Luoyi's research results of using Lianzong's "cut off self-finger", and then began to study the practice of eliminating self-fingerprints.
Unexpectedly, the Xueguo faction, which has always been indisputable, has also revealed its intention to end at this moment.
The current leader of the Xueguo faction, "Snow Guozhu" Ke Moge [Andrei Kolmogorov] also published a new paper.
He made a completely new narrative about the theory called "achievability".
The Xueguo School is also a model of Lian Zong, and is also subordinate to the "Intuitionist School."
However, there is a subtle difference between the "intuition" of the Xueguo school and the "intuition" of Shujun.
In fact, different monks have different ideas about the structure of "intuition".
Xue Guozhu's thesis indicates a strange fact. For any proposition, there is a corresponding non-proposition, and if the non-proposition holds, it means that the proposition is absurd. The proof of a non-proposition is a function that transforms the proof of the proposition into a ridiculous proof.
Absurd standard examples can be found in arithmetic. Assume 0 = 1, and perform mathematical induction: 0 = 0 is obtained by the equivalent axiom; (induction hypothesis) If 0 is equal to a specific natural number n, then 1 will be equal to n + 1, but because 0 = 1, so 0 is also equal to n + 1; by induction, 0 is equal to any number, so any two natural numbers are equal.
This is obviously absurd.
Perhaps in natural language, this is a low-level joke? But in arithmetic, it does have an important position.
At almost the same time, another Lian Zong Xiaoyao monk also independently completed a similar result.
He rewrote the important achievement of Lizong, an axiom of arithmetic, in a strange form that Lizong monks seemed to have.
This time, the entire Wan Famen began to become chaotic.
All monks who use research mathematics theory are caught in thinking about three issues.
Where am I from? Is it a sect or a sect?
What am I studying? In which direction?
—Who is my teammate? Geting School? Feng Luoyi? Kipai? Snow country? Or Shaoli?
This is unprecedented chaos.
Although in history, Lianzong will absorb the achievements of Lizong and Lizong will absorb the achievements of Lizong, but that is all based on "transforming to a mathematical basis".
Take geometry fusion arithmetic to analyze the geometry of containment, like this.
But now, it is completely chaotic. Lizong and Lianzong have never competed with each other for such a field. They are almost doing research in the form of relay running.
After you research a paragraph, I continue to research a paragraph on your basis, and then you research on my achievements.
After the disintegration of several Lizong families in the Middle Ages, such chaos appeared for the first time in 40,000 years.
The division between Lizong and Lianzong is still very obvious, but the research is in a mess.
It can be said that they are in chaos.
In particular, the Xue Guo faction, which has always been beyond detachment and struggle, and the fundamental faction, which has always been strong despite its recent establishment, are forces that cannot be ignored.
The same as Lian Zong, there are also differences between the Xueguo faction and the Shaoli faction.
Both are secular, and the relationship between Kipai and Geting factions is not harmonious.
Everyone killed each other in a ball.
Even some extreme disciples finally began to no longer separate Zong Lianzong.
Any disciple who is different from ours can be regarded as an "enemy"!
With the melee at the theoretical level, the Wanfamen finally finally lost its stability.
Even the maintenance of the rules of the gate rules, there is no way to maintain pure gravity.
The master Chen Jingyun had to urgently transfer a number of law enforcement officers from other schools to maintain the basic stability of the Wanfa door.
Seeing this situation, Zhao Qingtan was a little confused: "I just came to buy flour ... I just want to have a good year!"
"It's still a year of farts!" Su Junyu gritted his teeth: "This is bullying us and the faction is no one ... bullying us away from the sect!"
"... No, I don't think the supporters of the Geting school like Kepie very much."
"It doesn't matter!" Su Junyu waved his hand: "Now, the most notable thing is that Lian Zong, who is called Hai Ting [Arand Haiting], is free."
Although Hai Ting is also free, it probably belongs to the infamous individual. He proved impunity more than ten years ago. At that time, it was the fortune-teller who was in full swing, after the implementation of the yuan calculation in all methods. The glory of Hai Ting's generation of monks was almost overwhelmed by the fortune teller.
No, even if he doesn't count, he won't be too dazzling. As long as Shujun is still alive, all the other intuitionists, even monks, can only count as stars-and Shujun is just like Haoyue.
However, now, this little-known pastime has independently completed similar content with Xue Guozhu, and even rewritten the arithmetic axiom.
Although the axiom of arithmetic also has hidden dangers on the basis of incompleteness and undecidability, it is not as sure and complete as the axiom of drawing sky [Euclidean geometry axiom], but in the past, it was the glory of the sect.
As a Linzong, his logic of absorbing Lizong was so successful that he almost opened up a new way.
"So what are you going to do? Also come to an end?" Zhao Qingtan asked in return: "Wang Qi should have lost his interest in this debate, and the paper was only published at the right time. Kipai will not go deep into it. Going in this debate. "
He was too clear about Wang Qi's research ideas. Kipai is just focusing on the "foundation". That paper is a larger part of the puzzle, not thrown out for controversy.
"Well, I understand this very well." Su Junyu nodded and looked at his hand.
Although he only communicated with the paper through letters, he gradually realized some things in the past few years.
Wang Qi has set his sights on a higher area. For him, "wrong calculation" is already a thing of the past. He wanted to go beyond these things, go to a higher realm, and see the wider beauty that he had learned.
Not just basic mathematics, this material world is the same.
The picture that Wang Qi completed in the underground, after all, needed an extremely surprising and extremely beautiful arithmetic theory to support it.
Although it's a bit weird to say so ... at this point, he is a bit similar to Shujun.
"Is it enough to complete my obsession?" Su Junyu smiled: "I have recently read the papers of Geting School and Senior Feng. I do have some ideas ... I have perfected basic school arithmetic in recent years, and my level is also good. Is it up already? "
"Hey, what do you want to do?" Zhao Qingtan frowned slightly: "Even if Hai Ting is more marginal, that's also the honor of Xiaoyao! Do you want to fight with the monk of Xiaoyao period?"
Su Junyu's mouth twitched: "Why should I go to a monk who is at ease?"
Zhao Qingtan was about to breathe a sigh of relief, Su Junyu continued to say: "Of course it is the Lianzong!"
"you……"
"Although it is not as good as the fellow Wang Qi, when I was a kid, I was indeed considered to be a talent with a runaway series?" Su Junyu said with a smile: "And, this melee, the source is still several years ago, our leaders are not good What about it? As a member of the school, I come to the end, is it well known? "
Zhao Qingtan no longer speaks.
So, Su Junyu began research before the year was over.
However, he followed the idea of ​​"relative consistency" given by the fortune-teller, looking for a different direction from the Geting School, and continued to climb.
In a blink of an eye, it was time for a new starship sailing to another country to set sail.
Zhao Qingtan brought a group of disciples to Shenjing.
Looking at the hometown city that had become familiar again behind him, Zhao Qingtan was a little trance.
This time, Su Junyu did not come out to give away.
Before leaving, he just asked Zhao Qingtan to bring some drafts. This is the result of his recent days.
Zhao Qingtan felt that the manuscript paper was unusually heavy.
I do n’t know what the future is waiting for Brother Su.
He took the newly-disciplined Wanfamen disciples to the starship.
He returned to his hometown.
After opening a welcome banquet for those new monks, Zhao Qingtan went to Wang Qi alone and reported on his achievements in the past six months.
In addition, the manuscripts of Su Junyu were presented.
When Wang Qi read it roughly, he was shocked: "Huh, actually ... this?"
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