"Arithmetic...... Incomplete?" After hearing this, Bo Xiaoya's first reaction was-why are you kidding me?

Is the learning incomplete?

How can arithmetic be incomplete?

Arithmetic must be complete!

Even those who are completely different from the arithmetic master agree with his famous saying, "We must know, we must know."

For the arithmetic master and his followers, the arithmetic must be complete and consistent. In the eyes of these monks, the ontology of arithmetic is the "form" of the combination of operators. Every statement made up of operators can be judged as "correct" or "wrong", and the correct statement must be proved by another combination of operators. In addition, there are always only two judgments of "true" or "wrong" in a statement. There can be no such thing as "both right and wrong" or "not right and not wrong".

Completeness, consistency, and decidability are the foundations of the beliefs of the Counters and the Gottingists.

For the average arithmetician, although this part is inevitable, they intuitively feel that arithmetic must be complete.

Those monks who have studied the laws of material circulation have been amazed countless times to discover that when they were thinking of launching an attack in a certain field, the arithmetic masters of the Ten Thousand Methods Sect had already prepared for them a "tool for seeking the Tao"—the formula of arithmetic. From the earliest Yuanli Sect, to the Guiyi Alliance, and then to the Ethereal Palace today, these sects that have explored heaven and earth through empirical evidence have been providing more and more formulas to the Ten Thousand Law Sect - exquisite formulas derived from all things in heaven and earth, and Taoism and nature. These formulas fed back the development of arithmetic.

In the eyes of the monks of the Ten Thousand Dharma Sects, everything in the universe moves respectfully according to the laws of arithmetic.

You say that arithmetic is incomplete. That is to say. There is a flaw in this world. Is there something wrong with this Heavenly Dao?

Bo Xiaofeng is more stable than his sister. He pressed Su Junyu's shoulder and crossed an internal qi: "Su Junyu, stabilize your mind and beware of ......the breeding of demons in your heart."

On the other side, a Yang God Pavilion Grandmaster couldn't sit still, and ran over and asked, "Do you need help?"

Su Junyu smiled, waved away Bo Xiaofeng's hand, and saluted the Yuan Shen Grandmaster. Said: "The disciple is very good, I am tired of this uncle." ”

After leaving all the monks of the Yang God Pavilion, Su Junyu's eyes burned and said, "I'm not crazy, I'm just explaining a possibility." ”

"Possibility? You call this a 'possibility'?" Bo Xiaofeng frowned: "Are you crazy?

"No one can deny this possibility until completeness is proven. Su Junyu said seriously: "We don't know ...... from beginning to end."

"This is the result of believing in the sect. Suo Wenhong frowned in disgust: "This is purely ...... It's ......"

For the disciples of Lian Zong, some things are self-evident and cannot be denied.

For the disciples of the departing sect, some things are inevitable, but they have not yet been proven. It cannot be denied.

Only on this point has the views of the sect and the sect have always been.

Qin Chuanhe also frowned: "What about the proof?"

Su Junyu shrugged: "For the time being." Not yet. ”

"Not yet, you dare to say such things......"

"It's not a formal occasion anyway," Su Junyu didn't care.

Bo Xiaofeng was curious: "Su Junyu, what kind of thinking are you?"

"I was thinking that this study must be to pave the way or buffer the new theory. However, what we are learning now is some 'axiomatic' or 'proof of the completeness of the axiomatic system'. These things, not to mention one or two hundred years ago, just a few years ago, there was a new breakthrough. It's definitely not a game-changer. Su Junyu said slowly: "Since what we are learning is not the subversive content itself, it must be the precursor of the subversive content, or something that can offset the impact of the subversive content." ”

Bo Xiaofeng nodded, indicating that Su Junyu's words were reasonable.

"Since that subversive theory must be related to what we have learned in the past few days, it is relatively simple to think from what we have learned in the past few days. ”

"And have you noticed, there is a peculiarity of what we are learning - they are all the product of 'a certain idea,' and they are all tricks to get around 'a certain wall.' ”

Bo Xiaoya immediately reacted: "Senior Brother Wang Qi said the train of thought seven years ago...... This trick is for the sake of ...... In order to bypass the proof of multi-order logical completeness!"

-- It's this Wang Qi again......

Qin Chuanhe's brows furrowed unconsciously: "What we have learned is a trick to bypass the multi-order logical completeness proof, so you guess that the arithmetic is incomplete?

"If the completeness is proven, then none of these things have any meaning!" Su Junyu retorted: "And the arithmetic is complete, and it does not contradict any of us's intuitive feelings!, then it is not considered 'subversive'!"

Suo Wenhong shook his head: "Unreasonable"

Qin Chuanhe roared in a low voice: "Prove! This idea, you must give proof!"

By the end of the conversation, almost everyone had left with resentment. And Su Junyu's brows furrowed deeply again.

Oh, yes...... Proof, proof must be given......

- But, Wang Qi, if you really did such a remarkable achievement, how did you prove it?

For the first time, Su Junyu felt a little powerless. He pondered the important truth of "incompleteness". Or is it because of the truth in Wang Qi's notes that "even the simplest numbers have meanings beyond human thinking". Let him come up with proof on his own......

Due to cognitive reasons, Su Junyu didn't realize that Wang Qi and Feng Luoyi had already hinted at the key to this proof to him.

"Blade Assassin", "Self-Referential".

In the end, Su Junyu also sighed deeply.

- Damn, I can't catch up with that kid's train of thought.

....................................................................................................................................

In the Ten Thousand Immortals Fantasy Realm, Feng Luoyi and Fairy Ruoche watched this scene throughout the whole process.

Ruoche Fairy had a sarcasm in her tone, nine points bitter: "It seems that your and Wang Qi's hard work has been in vain." No one realized that the mirage was the key to solving the puzzle...... Self-referential, self-referential...... Hehehe. ”

Feng Luoyi's tone was calm: "It's a good phenomenon after all." ”

Fairy Ruoche said, "What should I do next? Do you want to use more explicit hints?"

Feng Luoyi shook his head: "Not for the time being." The most important thing for us is to guide, to observe the transformation of these people's thinking processes. He paused, then said, "Observe for seven more days." If this suspicion shows no signs of being ignored or forgotten, then let the first group of Genshin monks join this training camp. ”

Ruoche Fairy smiled bitterly: "Looking at them one by one, they have clearly mastered the most critical key but are not allowed to enter, I feel as if I see myself...... For hundreds of years, he was like a headless fly, he didn't know anything, he ran around, but he didn't know that Baoshan was by his side. 'Alchemist Paradox', hehe, what an ancient theory. Self-referential ...... Self-referential ......"

In the end, all the emotion turned into a sigh: "Why didn't I think of it?"

"When people think about this problem, they will only fall into the labyrinth of layers of self and find it difficult to extricate themselves. However, there is a kind of genius who can cut through the falsehood and see the core of things. Feng Luoyi's tone was calm.

Gödel's incompleteness theorem, the proof of Wang's incomplete law, was not achieved overnight. It also requires a tortuous and difficult period of thinking.

"Wang Qi is that genius?"

"He's undoubtedly a genius. Seeing that Fairy Ruoche was not in high spirits, Feng Luoyi changed the subject: "Then again, how is Lord Ximen's side?"

"Master's side ......" Fairy Ruoche smiled bitterly: "It's probably because the obstacle is too terrifying." He was not aware of this aspect at all. And...... And ......"

Feng Luoyi frowned: "And what?

In fact, there was an idea within the Gotting. Ruoche Fairy was a little ashamed to speak: "They say that the expression and proof of the incomplete law are too arbitrary. The concept of 'incomplete arithmetic' is only four short words, but it is ...... Almost inexpressible. They felt that as long as they refused to admit that it was arithmetic, and regarded it as a 'play on words' in their hearts, they could ...... It can avoid the shaking of the Dao heart. ”

"Huh. Feng Luoyi showed a sarcastic expression: "This is how the king despises us, and now we still despise others in this way?"

Fairy Ruoche sighed: "But...... It is indeed not an arithmetic statement...... Perhaps, this idea can be used to protect the teacher......"

Feng Luoyi said angrily: "Do you want Lord Ximen to be that kind of gutless rat?"

Fairy Ruoche sighed: "It's not a complete law, and the persuasiveness is still a little insufficient. ”

..................................................................................................................

"It seems that the convincing power of the law of incompleteness does have some shortcomings......

This is what Wang Qi came up with after sending a spiritual message to Chen Youjia for the seventh time without success.

Gödel's law of incompleteness has shown extraordinary value in the philosophical realm of the earth. Together with the unfathomable principles of quantum mechanics, it forms the basis of human cognition in the new century. But on the other hand, it doesn't have that much mathematical significance. It is a milestone in mathematics, but it is rarely seen in the later fields.

Because, in the eyes of those who are more practical, Gödel's law of incompleteness is meaningless. In the eyes of those who are biased towards theory, Gödel's law of incompleteness is not mathematical enough.

"Shouldn't I add another fire......

If I add a little more fire, the teacher's resistance to pushing this theorem will probably be much smaller...... Yujia doesn't need to stay in the Ten Thousand Ways Gate anymore...... My plan will also be able to be implemented more quickly......

Wang Qi's mind gradually turned to this aspect.

If you want to say irrefutable persuasiveness......

"Shall I solve the first question of Simon's twenty-three questions?"

Wang Qi happened to know how to increase the persuasiveness of his theoretical system. (To be continued.) )