Into the Immortal Cultivation - Chapter 2077

[Chapter 90 Strange Phenomenon [Third]]

The undecidability of the semigroup word problem is the first undecidability problem discovered by human beings that is not made by mathematicians, but exists naturally.

It also means another reality.

“Undecidability is not just limited to pure arithmetic.”

It seems to emphasize the objectivity of the concept of “undecidability”.

Countless Lianzong cultivators were like mourning and examining their concubine. They simply cannot believe that the language that constitutes their own thinking also contains the danger of “undecidability”.

However, for a while, they couldn’t even find a reason to refute.

Because, in the field of “linguistics”, Wang Qi occupies a monopoly position, and he uses arithmetic and logic to deal with the problem of writing.

There is no doubt that this is an area of separation.

Lian Zong couldn’t even find a point to use his fists, so he couldn’t exert his strength.

“This… Feng Luoyi, Wang Qi, this pair of master and apprentice, are they going to join forces to destroy the family?”

Cultivator Lianzong shouted in horror.

However, compared to Lianzong, Lizong was equally uncomfortable.

This paper, however, once again emphasized the status of “undecidability”.

“This guy, in order to promote himself, so he will attack us?”

Lizong cultivator also gritted his teeth with hatred.

Wang Qi’s paper is undoubtedly a heavy punch, which slammed into the spine of Lizong cultivator.

This time, neither Li Zong nor Lian Zong benefited from it.

But soon, Lian Zong Xiaoyao responded.

Many Lianzong Xiaoyao have finished their current tasks in Zhengtian Division, and concentrated on preparing for this debate.

Now, within Lianzong, a new direction has gradually emerged.

They actually tried to learn Lizong’s “logic”, absorbed Lizong’s knowledge, and used Lizong’s theory to counter Lizong.

This should be regarded as a counterattack against Feng Luoyi’s use of Lianzong’s research results of “cutting off self-references”, and then began to study the practice of eliminating self-reference sets.

Unexpectedly, the Snow Kingdom faction, who has always been indisputable in the world, actually showed the intention of ending at this moment.

The current leader of the Snow Kingdom faction, “Snow Kingdom Lord” Ke Moge [Andrei Kolmogorov] also published a new paper.

He gave a whole new account of a theory called “achievability”.

The Snow Kingdom faction is also a model of Lianzong, and it is also subordinate to the “intuition faction”, and they will also hold the disciple ceremony for Jun Jun.

However, there are subtle differences between the “intuition” of the Snow Kingdom faction and the “intuition” of Shunjun.

In fact, different cultivators have different ideas about the structure of “intuition”.

Snow King’s paper points to a strange fact. For any proposition, there is a corresponding non-proposition, and if the non-proposition holds, it means the absurdity of the proposition. A proof of a non-proposition is a function that transforms the proof of the proposition into an absurd proof.

Standard examples of the absurd can be found in arithmetic. Assume 0=1, and perform mathematical induction: 0=0 is obtained by the axiom of equivalence; (induction hypothesis) if 0 is equal to a certain natural number n, then 1 will be equal to n+1, but because 0=1, 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 ridiculous.

Perhaps narrated in natural language, this is a low-level joke? But in arithmetic, it does have an important position.

And almost at the same time, another Lianzong Xiaoyao cultivator independently accomplished similar results.

He rewrote Lizong’s important achievements in arithmetic axioms in a form that Lizong cultivators looked a little weird.

All of a sudden, the entire Myriad Dharma Sect began to become chaotic.

All monks who study arithmetic theory are caught up in thinking about three questions.

Where am I from? Lianzong or Lizong?

What am I researching? In which direction?

Who are my teammates? Song court? Feng Luoyi? base? Snow country pie? Or Shaoli?

This is unprecedented chaos.

Although historically, Lianzong will absorb Lizong’s achievements, and Lizong will absorb Lianzong’s achievements, but it is based on “transformation into a mathematical basis”.

Fusing arithmetic with geometry to analytically accommodate geometry, like this.

But now, it’s all messed up, Lizong and Lianzong have never competed with each other for a field like this. They are doing research almost in the form of a relay run.

After you study for a period, I continue to study on your basis, and then you study on my achievements.

It was the first time in 40,000 years that such a chaotic scene appeared after the division of the Lizong and Lianzong of the Middle Ages.

The division between Lizong and Lianzong is still very obvious, but in research, they are united.

It can be said that they are purely fighting.

In particular, the Snow Kingdom faction, which has always been detached and fighting, and the base faction, which has always been aggressive despite its recent establishment, are forces that cannot be ignored.

The same as Lianzong, there are differences between the Xueguo faction and the Shaoli faction.

Both are from the Lizong, and the relationship between the Ji faction and the Geting faction is not harmonious.

Everyone killed each other.

Even some extreme disciples finally began to no longer distinguish between Zong and Lianzong.

All disciples of Wanfa Sect who are different from our side can be regarded as “enemies”!

With the melee at the theoretical level, Wanfamen finally gradually lost its stability.

Even the law enforcer who maintains the door rules can’t maintain pure gravity.

The sect master Chen Jingyun had to urgently transfer a group of law enforcement officers from other sects to keep the internal stability of Wanfa Sect basically stable.

Seeing this situation, Zhao Qingtan was a little confused: “I’m just here to buy flour… I just want to have a good year!”

“Have a good year!” Su Junyu gritted his teeth: “This is bullying our foundation. Pai No Man… bullies us from Lizong No Man!”

“…No, I don’t think the Ge Ting faction’s supporters are very fond of Ji Pai.”

“It’s not important!” Su Junyu waved his hand: “Now , The most notable one should be the Lianzong Xiaoyao named Hai Ting [Alander Haiting].”

Although Hai Ting is also Xiaoyao, he probably belongs to that kind of unreputable individual. He became free and easy more than ten years ago. At that time, it was just after the master of calculation was in full swing, after the implementation of yuan calculation in all ten thousand methods. The brilliance of the cultivator Lian Zong of Hai Ting’s generation has almost been overshadowed by the master.

No, even if he is not the master, he will not be too dazzling. As long as the Sovereign is still there, then all the other Intuitionist Lianzong cultivators can only count the stars and the Sovereign is like a bright moon.

However, now, this little-known Xiaoyao has independently completed similar content with Lord Snow, and even rewrote the axioms of arithmetic.

Although on the basis of incompleteness and undecidability, the axioms of arithmetic also have hidden dangers, which are not as definite and complete as the axioms of painting the sky [Euclidean axioms of geometry], but this was the glory of Lizong in the past.

As Lian Zong, the logic of absorbing Li Zong was so successful that he almost opened up a new path.

“Then what are you going to do? Are you going to end?” Zhao Qingtan asked back: “Wang Qi should have lost interest in this level of debate, and publishing that paper is just a coincidence. I went in this debate.”

He was too aware of Wang Qi’s research ideas. Fundamentalism just focuses on the “foundation”. That paper is a bigger piece of the puzzle than thrown out for debate.

“Well, I understand this very well.” Su Junyu nodded and looked at his hand.

Although he only communicated through letters and papers, over the years, he has gradually realized something.

Wang Qi has set his sights on a more distant area. For him, “ill-conceived calculations” are a thing of the past. He wants to transcend these things, to go to a higher realm, to see the wider beauty of mathematics.

Not just basic arithmetic, but also the material world.

The picture that Wang Qi completed in the underground, after all, needs an extremely surprising and beautiful mathematical theory to support it.

Although it’s a bit strange to say that… In this respect, he is somewhat similar to Jun Shun.

“Is it a completion of my obsession?” Su Junyu smiled: “Recently, I read the papers of the Ge Ting School and Senior Feng. I do have some ideas… After years of perfecting the basic arithmetic, my level has risen?”

“Hey, what do you want to do?” Zhao Qingtan frowned slightly: “Even if the real Hai Ting is marginal, then It’s also the honor of Xiaoyao! Do you want to fight with

a monk in the free period?” Su Junyu twitched his mouth: “Why should I go to a monk in the free period?”

Zhao Qingtan was about to breathe a sigh of relief, and Su Junyu continued: ” Of course it’s Lianzong!”

“You…”

“Although I’m not as good as Wang Qi, but when I was a child, I was indeed considered to have the talent of the unhurried series, right?” Su Junyu laughed: “Also, this melee , the source is still several years ago, what about the miscalculation of our leaders? As a member of the base faction, I am a famous teacher, right?”

Zhao Qingtan stopped talking.

So, before the end of the year, Su Junyu began to study.

However, he followed the idea of “relative consistency” given by the master, looking for a different direction from the Ge Ting school, and continued to climb.

In the blink of an eye, it was time for a new starship bound for a foreign country to set sail.

Zhao Qingtan brought a kind of disciple to Shenjing.

Looking at the hometown that he had become familiar with behind him, Zhao Qingtan was a little dazed.

This time, Su Junyu did not come out to send them off.

Before leaving, he just asked Zhao Qingtan to bring some drafts with him. This is the result of his recent days.

Zhao Qingtan felt that the manuscript papers were unusually heavy.

I don’t know what kind of future awaits Junior Brother Su.

He took the Wanfa disciples who had newly joined the base faction and boarded the starship.

He returned to his hometown.

After holding a welcome banquet for the newly joined monks, Zhao Qingtan went to Wang Qi alone and reported on his achievements in the past six months.

In addition, Su Junyu’s manuscripts were presented.

Wang Qi read it roughly, and was shocked: “Tsk tsk, it’s actually… this?”

[End of this Chapter]