Vol 3 Chapter 859: Gödel's proof

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"I know! I know!" Su Junyu's excited voice spread throughout the training ground. He roared with excitement, shattering the manuscript in front of him with force, and threw it into the air, almost like a maiden scattered flowers.
In recent days, this training ground has been lifeless. A group of mathematicians whose beliefs are destined to be rejected are learning and communicating together, just like a group of dead prisoners holding groups to warm up.
Su Junyu's voice undoubtedly gave a great encouragement to others.
Bo Xiaofeng was shocked. He knew what Su Junyu was thinking. Although all the signs indicate that some predecessors may have proved that it is "incomplete"-if not, at least it will negate the idea of ​​the owner.
However, when this result was really presented to him, he could not believe it.
Su Junyu's appearance also attracted the attention of others. In the past few days, his strange thought has been known to many people. I heard that he was thinking about "incomplete" things, many people stared secretly. Or wait to see the joke, or wait for his success.
And now, he succeeded?
More people surrounded Su Junyu. Bo Xiaofeng first reluctantly said: "Su Junyu ... Congratulations ... Congratulations ..."
Su Junyu waved his hand: "It's not congratulations yet. I feel that I have inadvertently found a major direction ... If successful, Yuanshen is hopeful."
Another monk who knew Su Junyu asked: "Yuanshen ... you have just been Jin Dan for three or four years now?"
"The way of Yuanshen. No, if I really solved this problem, maybe even the Yuanshen, even the practice of Nirvana is a stubborn thing." Su Junyu's expression was extremely excited: "This may be a level of freedom Results! "
Everyone took a breath.
Before and after the Yuanshen Tianguan, make the achievements of the pastime period, and then promote the pastime smoothly and smoothly. There are many such monks. Tai Tianzun is a typical example. This is the case for many talented monks who have become famous for many years.
Everyone looked at Su Junyu's eyes and immediately changed. The achievements of the Xiaoyao level mean an infinitely bright future. Even if it fails in this direction, it is not a wrong path. In this "negation", the monk who initiated the shock can also obtain huge benefits.
Moreover, what can be achieved at this time, in addition to the second question out of twenty-three questions-"completeness proof", what can it be?
"Did you find your way?" Gao Jiyang hurriedly asked. Although he has changed his thinking, he has not yet found a way to incompleteness.
Su Junyu nodded and said, "Yes. But declare in advance, you can't this idea."
"Brother Su, if so many people are watching, I don't believe there are people who are ashamed." Bo Xiaoya said loudly. She was impatient for the incomplete proof, and she waited to see the proof.
Bo Xiaofeng also said: "Yes. Old Su, if someone will plagiarize your ideas, I ... and my family will support you."
The "family" that Bo Xiaofeng said, but that is the entire Bo family including mostly monks. No one can ignore this warning.
And more people shouted: "Maybe it is something that has been proved by that predecessor, as for hiding it? Hurry up! Hurry up!"
The answers to these questions have long been awaited by these disciples
Su Junyu nodded: "Okay, then I will talk about it. Do you know the continuum?"
"Continuum?" Gao Jiyang immediately noticed that something was wrong: "Does the second question also involve continuum? The first and second questions are actually two sides of the same question?"
Su Junyu also froze: "Ask two questions? Is there such a saying?"
Immediately, he also realized something, and said with a cry of laughter: "That ... I'm sorry everyone, my inspiration just now is the first question, not the second question."
"First question?" Bo Xiaofeng's eyes widened: "Aren't you thinking about the second question? How come to the first question again?"
"Just hit by mistake." Su Junyu laughed: "In order to deny the completeness, I have been thinking about every corner of mathematics that I can think about, especially in the system of set theory. Then, I thought about the" set axiom " , From that axiom, I found inspiration ... "
"Stop!" Gao Jiyang stopped Su Junyu, and then drew a circle in the air with his fingers. Heaven and Earth Aura gathered in this circle along with his will, and turned into a mature law. This aura of light encircled the people around Su Junyu.
Gao Jiyang said in a deep voice: "We may be able to guess that the second question has been solved. However, there is no sign that the first question has also been solved by others. Therefore, this idea should belong to Su Shidi alone. . "
"If the brothers and sisters around you are still doing research in the field of the first question, and if you want to have a face, it is best not to listen. Otherwise, if there is a dispute in the future, everyone will not look good on the face.
After a while, two or three masters of Yuanshen period retreated from Gao Jiyang's circle. The role of this aura is to isolate internal and external induction. As long as they are out of this circle, Su Junyu will not hear and see no matter what they talk about.
If they and Su Junyu really have similar inspirations, then it is really unclear. Especially Su Junyu seems to have a good relationship with the two siblings of the Bo family. If it were because of this, it left a bad impression in the eyes of the behemoth, the Bo family, that would be a great loss.
At this time, Gao Jiyang said to Su Junyu: "Brother Su, you can continue. However, don't say too much, click to the end."
Su Junyu smiled and touched the back of his head: "Senior Brother's heart is too much, and Meng Lang has been out for a while, and Brother has learned something."
"Fortunately, my field has nothing to do with the first question, otherwise I certainly can't help but want to listen." Gao Jiyang laughed: "Now you just talk about it."
"Tell me!" The people said indignantly.
"Then I will talk about it. First of all, I want to explain that this is just my current idea, an idea. I don't have a specific process, and I don't know whether the predecessor theory of this process is perfect."
"I think so. First of all, we have to build a framework, and then all set sets that are allowed by the axioms of set theory are placed in this framework. Then within this framework, let's do this again ... "
Su Junyu's surroundings gradually became quiet.
"Now, let me rethink the continuum."
After finishing the communication with Lu Xiaoqian, Wang Qi sat back at his desk and began to think about the issue of continuum proof.
"First of all, it is Gödel's proof of the problem."
"Gödel's job is to build a huge framework. Within this framework, it contains all the 'buildable sets' in all ZF axiom systems. Then, in this model, Gödel proved that within the ZF axiom system The continuum hypothesis cannot be falsified. "
"And twenty-three years after Gödel made this proof, another scientist, Cohen, made a proof. This proof proves that within the ZF axiom system, the continuum hypothesis cannot be confirmed."
"In other words, the continuum hypothesis is actually an undecidable problem. It is independent of set theory. Whether it is true or false, whether you accept it or not, it does not affect anything."
"The famous hypothesis set by the founders of set theory based on set theory is independent of set theory, which is considered to be artificial." Wang Qi exclaimed slightly.
"The forced method is very different from Gödel's thinking."
The "force method" is quite violent. In fact, its idea is very close to violent cracking. It expands the range of "buildable sets" to the minimum range allowed by the ZF axiom system, and then gradually approaches that result.
Since this argument involves "creating collections that did not originally exist," Cohen's force proving process is many times more difficult than Gödel's process.
And this is the most critical part. The "force method" is not just about continuity. Its appearance allows mathematicians to discover many other propositions independent of the ZF axiom system.
From a purely mathematical point of view, the impact of the forced method is even greater than Gödel's incomplete theorem.
In the history of the earth, some mathematicians led by Hilbert ignored Gödel until they died. Of course, a large part of the reason is the dispute between ideas and beliefs. They simply cannot accept Gödel's theory.
However, this is also related to Gödel's argument "not enough math".
In the view of some mathematicians, Gödel's incomplete theorem is more of a textual argument than a mathematical proof process.
"As long as I can complete the forced law, Shenzhou's mathematics can enter a new realm."
Wang Qifen wrote a disease book. All of a sudden, there was only the sound of the nib rubbing against the paper.
"Look for ... Look for a set that is smaller than the set that can be built under the ZF axiom ..."
"Independent axiom ..."
"independent……"
In Wang Qi's thinking, the mana inside him changed slightly again.
Only this time, there were no visions around him, nor any signs of riots or collapses in mana.
All changes seem to be silent. It seems that his mana has been adjusted a little bit.
Wang Qi himself did not know what effect this new adjustment had.
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