Into the Immortal Cultivation

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"The next thing I want to talk about is the most important concept I learned from the work of Lord Jimen and the Gotting School! Formalization."

As soon as Wang Qi's words came out, Junjun's brows increased.

Behind him, more Shaoli sentiments were almost outraged.

There are countless achievements in the life of Hippocher. However, his views on the nature of mathematics are widely criticized, which is difficult for most mathematicians to accept.

From the perspective of the operator, the essence of arithmetic is "form". The individual symbols have no meaning. Those "forms" where the symbols are arranged are the mathematics.

This is like saying that in the initial formula of "1 + 1 = 2", the symbols "1", "+", "=", and "2" are meaningless, and only the complete equation has mathematics. significance.

On the other side, many counties of Geting School are also in a mixed mood. A strange expression appeared on their faces, mixed with confusion and anger.

The concept of "form" includes consistency, completeness, and decidability. It can be said to be the greatest pursuit of the ideal Yu Yu who is the fortune teller.

It was Wang Qi himself who rejected this ideal.

Wang Qi's use of the operator's ideas rejected the operator's pursuit and also rejected the decades of efforts of the Geting School.

However, these complex feelings did not affect Wang Qi.

Wang Qi understands that what he represents now is not himself, but "correct".

Self-referentiality is not a mathematical description—it really belongs to logic, but whether it belongs to mathematics remains to be discussed, and not all mathematicians recognize this. Both the earth and China have such signs.

"This statement cannot be proved" is not a mathematical statement in a narrow sense.

The second step of Gödel's proof method is to convert this non-mathematical statement or quasi-mathematical statement into a mathematical statement.

The earth called it-"Gödel's digitization".

——Perhaps in Shenzhou, it will be called “Wang Qi Digitalization”, right?

"When the average person understands this incompleteness, it is easy to fall into the fog of heavy self-references, which is difficult to extricate themselves. I guess this is probably related to Senior Kang's diagonal proof method and the infinite cardinal number violate my natural intuition . It is precisely this important reason, so for thousands of years, our predecessors will ignore this important principle. "

"Instead of unraveling this heavy fog, this formal approach must be used."

Wang Qi released the golden light with both hands, and turned into a heavy light curtain, and countless operators flew and arranged on it, listing a great proof.

The second part of Gödel's proof of the incompleteness theorem, which is also its greatest part, is here.

"Any axiom system, the operators used, and the axioms that can exist are limited. Therefore, these axioms, the statements that these operators can list, must also be countable-infinitely countable, The number of Tao Yuan is zero, the number of natural numbers. That is how it is described. "

"And the length of these possible statements must be countable. And since it is still in the countable endless category, we can number it with natural numbers. Each number is unique."

"Then we can create a set" Zhongtian ". This set" Zhongtian "includes all possible" numbers ". Within an axiom system, all possible statements must be in this Within the number. "

...

By the time the sermon is here, it has begun to break away from what most people can understand. What is "countable infinity", what is "cardinal number" and "ordinal number". These have exceeded their understanding.

Even those monks who had shown off at the scene listening to Wang Qi preached, and some of them showed confusion.

They can understand every step the young man said. But what does it mean after these things are put together?

totally do not understand!

More of this Fa-cultivation to watch this "live broadcast" with the help of Wanxian Fantasy Realm, all of them were dizzy. This seemingly simple proof seems to contain infinite magic, as if to drag their thinking to an abyss.

Feng Luoyi had to sigh and explained to all the monks who watched through the live broadcast in the form of "subtitles".

This process of digitization is plainly a "mapping".

The symbols, expressions and sequences of expressions in the arithmetic system are all mapped to numbers-the introduction of "Gödel numbers" enables the digitization of objects. As a result of this processing, for mathematical logic and other related branches, a digital tool is provided in the research method, which can easily convert some discussion objects into natural numbers or functions of natural numbers. problem.

Transform a quasi-mathematical statement into a statement with mathematical meaning.

This is what this "digitalization" means.

And when this proof entered the second half of the second stage, in the song court, Ike sighed softly: "Original recursive ..."

His expression contained full regrets and regrets.

——I have also studied this field ... If I could go deeper in those days, would I be able to avoid today's disaster?

Several Geting monks immediately sent a private chat: "Brother Ai, do you have research in this field? Can you trip Wang Qi at this step?"

Ike shook his head with a wry smile. Wang Qi did nothing wrong in this step. Can he say what is right is wrong?

At the same time, he also made up his mind to go back and study this area that was not valued in the past,

Of course, the people present did not know that this digital proof has more meaning than itself.

It is also the source of recursion theory.

Recursion theory is one of the most important branches of modern logic.

At this point, Wang Qi's proof came to an end.

Wang Qi waved his hands for the last time. The arrangement of operators becomes a proof of incomplete theorems.

"This is the whole process."

The audience was silent.

Mathematics is going to death at this moment.

"Consistency and completeness are incompatible. There is no contradiction and completeness in learning ..." Many of the disciples who watched the live broadcast almost cried.

After Wang Qi had finished proving the incomplete theorem, he sat at the edge of the pulpit for a while. Today's preaching is divided into four parts. The previous part is about the incomplete theorem, and the next part is about the undecidable theorem.

Then, it is the time for questions and conclusions.

Those carefree monks also need a certain amount of time to absorb and understand these things.

He closed his eyes and nourished himself, and seemed to be completely unaware of the malice that the surrounding overhauls had imposed on him.

What if it's all enemies? This is the realm of seekers, not the occasion of fighting. If you say breaking the sky, it is impossible to reverse right and wrong.

After a short break, Wang Qi walked back to the center of the rostrum. The whispers of whispers that appeared as a result of short repairs gradually disappeared. The attention of countless monks focused on Wang Qi.

Like one after another poisonous snake, looking for the prey, trying to kill.

Wang Qi continued to preach: "After speaking about‘ incompleteness ’, let ’s talk about‘ whatever ’— that is, the undecidable theorem.”

"The first part of the undecidable theorem is the same as the incomplete theorem, it is" self-referential ", I will not repeat them here. I will go directly to the second part of the proof of the undecidable theorem."

"First of all, here, I need to thank Real Turing, thank him for his help on this issue, and thank him for an equivalent proof method."

"First of all, the first proof method that I want to introduce is that I put forward by the mechanism of the narrow Turing calculator ... And the second part, Turing is called" the universal method ". It It is constructed according to the incomplete theorem, a complete and inconsistent algorithm. "

This is also the part that Wang Qi and Turing live talk about.

The narrow Turing algorithm and the omnipotent method—that is, the Turing machine and the lambda algorithm—like the second stage of the second half of the proof of the incomplete theorem, have the potential to surpass the proof itself. In later generations, they each developed a leafy road.

Real Turing is also very happy that his not-so-favorable theorem can be spread. Wang Qi also needs the support of some **** monks to make him seem less powerless, so that more mathematicians can follow him and create a new world of computing.

The two can be said to be a hit.

The proof process of undecidable theorems seems to be much easier to deal with than that incomplete. Especially the first part, Turing machine proof. This story is almost the same as the "puppet examiner" Wang Qi previously told, and the phantom "Silver Wing Assassin".

Many monks who do not belong to the Ten Thousand Fas, especially those small schools that use "literary art" and "fictions of novelists" as their practice, all listen to it with relish. They can't understand Wang Qi's theory, or the mathematical meaning behind Wang Qi's theory. However, they can understand the story! There are almost endless stories in their minds.

It is foreseeable that in a period of time in the future, "puppet people" will become a popular theme among the storytelling population.

The disciples of Wan Fa Men who have not yet collapsed have shown greater interest in the second method.

Bo Xiaofeng is in a state of coercion. "Complete but contradictory system"? Does such a thing really exist? Is there any meaning in this?

Wang Qi's narrative started from noon and clocked from unitary time. When the bell of unitary time struck in the land of China, this time the sermon also came to the end.

"In summary, we can make such a proof ..." Wang Qi took a deep breath and said the last two sentences.

"I think we can proudly announce that the most critical second question among the twenty-three questions of Jimen and the tenth question have been satisfactorily solved. Among the basis of arithmetic, the most important consistency, completeness and decidability Prove that it has been completed. "

"Study, you have to enter a new era."

No one applauded.

However, everyone feels-a revolutionary change, maybe it is really coming ...

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