Enter the Immortal Cultivation

"I know! I know!" Su Junyu's excited voice spread throughout the training ground. He roared wildly, and excitedly shattered the manuscript in front of him with his magic power, throwing it into the air, almost like a fairy scattering flowers.

In recent days, this training ground has been dead. A group of mathematicians whose beliefs are destined to be rejected study and communicate together, just like a group of death row prisoners huddling together for warmth.

Su Junyu's voice undoubtedly gave a great encouragement to others.

Bo Xiaofeng's body shook. He knew what Su Junyu was thinking about. Although all signs indicate that perhaps there have been predecessors who have proved that "incomplete" - even if not, at least it has denied the master's thinking.

However, when this result was really presented in front of him, he was a little bit unbelievable.

Su Junyu's appearance also attracted the attention of others. In recent days, his weird thoughts have been known to many people. Hearing that he was thinking about "incomplete" things, many people were watching secretly. Either waiting to see a joke, or waiting for his success.

And now, he succeeded?

More people gathered around Su Junyu. Bo Xiaofeng was the first to reluctantly say, "Su Junyu... Congratulations... Congratulations..."

Su Junyu waved his hand: "It's not time to congratulate yet. I feel like I have accidentally found a major direction... If I succeed, there is hope for the Yuanshen."

Another cultivator who knew Su Junyu asked, "Yuanshen... You have only been in the Jindan stage for three or four years, right?"

"The path of the Yuanshen. No, if I really solve this problem. Maybe in addition to the Yuanshen, even the Lianxu Nirvana is a sure thing." Su Junyu's expression was extremely excited: "This may be a free and easy achievement!"

Everyone took a breath of cold air.

There are many cultivators who make free and easy achievements before and after the Yuanshen Tianguan, and then steadily advance to the free and easy stage. Tai Tianzun is a typical example. Many talented cultivators who became famous at a young age are like this.

The eyes of everyone looking at Su Junyu were immediately different. Free and easy achievements mean an infinitely bright future. Even if you work hard in this direction but fail. That is also denying a wrong path. In this "negation", the cultivator who launched the attack can also gain huge benefits.

Moreover, what other free and easy results can appear at this time, except for the second question among the twenty-three questions - "completeness proof"?

"Have you found the idea?" Gao Jiyang asked hurriedly. Although he has changed his thinking, he has not found the idea leading to incompleteness.

Su Junyu nodded and said, "Okay. But I have to make it clear in advance. You can't take this idea away."

"Brother Su. So many people are watching, I don't believe there are still people who are really shameless." Bo Xiaoya said loudly. She has been impatient for the incomplete proof and is waiting to see the proof.

Bo Xiaofeng also said, "That's it. Old Su, if someone plagiarizes your idea now, I... and my family will support you."

The "family" that Bo Xiaofeng said. That is the entire Bo family, including many free and easy cultivators. No one can ignore this warning.

More people shouted: "Maybe it has been proven by that senior, why is it hidden? Come on! Come on!"

These Wanfamen disciples have been looking forward to the answer to this question for a long time

Su Junyu nodded: "Okay, then I'll tell you. You know the continuum, right?"

"Continuum?" Gao Jiyang immediately realized something was wrong: "Does the second question also involve the continuum? The first and second questions are actually two sides of the same question?"

Su Junyu was also stunned: "One question, two sides? Is there such a saying?"

Then, he realized something and said with a smile : "That... I'm sorry, everyone. The inspiration I just had was from the first question, and has nothing to do with the second question."

"The first question?" Bo Xiaofeng widened his eyes: "Aren't you thinking about the second question? Why did you go to the first question again?"

"It was just an accident." Su Junyu laughed: "In order to deny completeness, I have been thinking about every corner of mathematics recently. Especially in the system of set theory. Then, I thought about the 'set axiom', and from that axiom, I found inspiration..."

"Stop!" Gao Jiyang stopped Su Junyu, and then drew a circle in the air with his finger. The spiritual energy of heaven and earth gathered into this ring according to his will, turning into a mature law. This spiritual light circle surrounded the people around Su Junyu.

Gao Jiyang said in a deep voice: "We may guess that the second question has been solved by someone. However, there is no sign that the first question has been solved by others. Therefore, this idea should still belong to Junior Brother Su alone."

"If the fellow disciples around you still want to do research in the field of the first question, and you still want to save face, it is best not to listen. Otherwise, if there is a dispute in the future, everyone will lose face."

After a while, two or three masters in the Yuanshen period withdrew from Gao Jiyang's circle. The function of this spiritual light circle is to isolate the internal and external induction. As long as they leave this circle, they can't hear or see anything Su Junyu talks about.

If they really have similar inspirations with Su Junyu, then it is really hard to explain. Especially since Su Junyu seems to have a good relationship with the two brothers and sisters of the Bo family. If they leave a bad impression in the eyes of the giant Bo family, it will be a big loss.

At this time, Gao Jiyang said to Su Junyu: "Junior Brother Su, you can continue. However, don't say too much, just stop talking."

Su Junyu smiled and touched the back of his head: "Junior brother's heart went too far, and he was so angry for a while. Senior brother taught him a lesson."

"Fortunately, my field has nothing to do with the first question, otherwise I would not be able to help but want to listen." Gao Jiyang smiled and said, "Now you can just talk about it."

"Tell me about it!" everyone said angrily.

"Then let me talk about it. First of all, I want to explain that this is just an idea and a train of thought that I have now. I don't have a specific process, and I don't know whether the prerequisite theory of this process is complete."

"This is what I think. First, we need to establish a framework, and then all established sets that are allowed to exist by the axioms of set theory are placed within this framework. Then within this framework, we will perform such operations... "

The area around Su Junyu gradually became quiet.

"Now, I'd better think about the continuum again."

After finishing the exchange of letters with Lu Xiaoqian, Wang Qi sat back at his desk and began to think about the proof of the continuum.

"First, there is Gödel's proof of this problem."

"Godel's work is to build a huge framework, which contains all 'establishable sets' in all ZF axiom systems. Then, in this model, Gödel proved that within the ZF axiom system, The continuum hypothesis cannot be falsified.”

"Twenty-three years after Gödel made this proof, another mathematician Cohen made a proof. This one proved that within the ZF axiom system, the continuum hypothesis cannot be verified."

"In other words, the continuum hypothesis is actually an undecidable problem. It is independent of set theory. Whether it is established or not, and whether you accept it or not, it does not affect anything."

"The famous hypothesis proposed by the founder of set theory based on set theory is independent of set theory. This can be regarded as a trick of fate." Wang Qi sighed slightly.

"The forced method is completely different from Gödel's idea."

The term "force method" is quite violent. In fact, its idea is very close to brute force cracking. It expands the range of "establishable sets" below the minimum range allowed by the ZF axiom system, and then gradually approaches that result.

Since this argument involves "creating a set that does not originally exist", the proof process of Cohen's forcing method is many times more difficult than Gödel's process.

And this is also the most critical part. The meaning of "force method" is not just a continuum. Its emergence allows mathematicians to discover many other propositions that are independent of the ZF axiom system.

From a purely mathematical perspective, the impact of the forcing method is even greater than Gödel's incompleteness theorem.

In the history of the earth, some mathematicians, headed by Hilbert, ignored Gödel until their death. Of course, a large part of the reason is a dispute over ideas and beliefs. They simply cannot accept Gödel's theory.

However, this is also related to Gödel's discussion being "not mathematical enough".

In the view of some mathematicians, Gödel's incompleteness theorem is more of a literary discussion than a mathematical proof process.

"As long as I can pass the force-forcing method, China's arithmetic will enter a new realm."

Wang Qi wrote vigorously. For a moment, the only sound in the study was the sound of pen tip rubbing against paper.

"Looking for... looking for a set smaller than the set that can be established under the ZF axiom..."

"The axiom of independence..."

"independent……"

While Wang Qi was thinking, the mana in his body changed slightly again.

Only this time, there were no strange phenomena around him, nor did his mana show any signs of riot or collapse.

All changes seemed to be silent. It seemed that his mana had undergone a slight adjustment.

Wang Qi himself didn't know what effect this new adjustment had. (To be continued ~^~)

PS: At the end of the month, please vote for me.