Enter the Immortal Cultivation

There was an alchemist in a certain sect who once made a bold statement: "My alchemy skills are very superb and well-known throughout China. I will make alchemy for all those in the Immortal Way who do not want to make alchemy for me, and I will only give it to these people." Make alchemy!" There was an endless stream of people coming to him to make alchemy, and naturally they were all those who couldn't make alchemy on their own. However, one day, the alchemist felt that his cultivation had stagnated, and he instinctively opened the alchemy furnace. So, could he make alchemy for himself?

This is the famous alchemist's paradox. If it is replaced by the low version of the non-magic plane, it will be the alchemist's paradox. If you want a more elegant expression, then there is an equivalent expression - Russell's paradox.

Suppose the property P(x) means "x does not belong to x", and now assume that a class A is determined by the property P - that is, "A={x|x?x}". So the question is: Is it true that A belongs to A? First, if A belongs to A, then A is an element of A, then A has property P. From property P, we know that A does not belong to A; secondly, if A does not belong to A, that is to say, A has property P, and A is composed of all It consists of classes with property P, so A belongs to A.

This is the dilemma that logicians cannot get around: Is the whole of a thing also a part of it?

This problem causes the inconsistency of set theory.

There are many ways to avoid this paradox, and Wang Qi knows two. Zermelo-Frankl axiom system [ZF system] and von Neumann-Börness-Gödel [NBG system]. The former is to limit the method of operating sets, and the latter is to realize the separation of sets and classes. These are the efforts, or struggles, of earth mathematicians on this issue.

"As long as set theory cannot be self-consistent, you will never give up - well, I admit it, even if set theory is self-consistent, it will not make any sense to him. To him, this is an empty concept. "It's a word game." Wang Qi crouched in front of the study and read Suanjun's paper again: "And to prove that set theory is complete... Am I stupid? I know that this road is incomplete, but I still go there. Prove this?"

Although this review paper by Suan Jun is more of a provocation and a declaration, the author is one of the greatest mathematicians in China after all, and it still has academic value.

For Wang Qi, the greatest value of this paper is that it sorted out some of the most critical problems currently encountered in Chinese arithmetic logic.

He held a pen in his hand, but instead of writing, he turned it around with a few fingers.

Almost all arithmetic can be deduced with a small amount of logic - but in the eyes of Suanjun, this is not arithmetic at all. In this case, no matter what results Wang Qi makes, he will be regarded as "more funny tricks" by the other party.

Well, here on Earth, such debates can easily devolve into endless nitpicking and personal attacks. Mathematics cannot produce an irrefutable result through experiments, and the debate will basically become a quarrel in the later stages. For example, historians of mathematics on Earth have rudely accused David Hilbert and Ruiz Brouwer of "lack of character to confine their battles to academic fields." The consequences of not being compensated.

"In China, everyone will probably do it in a more violent way, right?" For some reason, Wang Qi felt a little excited when he thought about the battle between Wanfamen Xiaoyao.

The essence of this debate is actually to increase one's own confidence, and then go all out to find loopholes in the other party's other theories, attack the other party's academic status, or do similar research to the other party, prove one's attainments in mathematics and completely crush the other party. , until one side loses all its confidence and surrenders voluntarily, and then the other side automatically wins.

Of course, there is also a slightly shameless method in the earth's academic community - the young side waits for the old side to die of old age and let time "prove everything". But in China, this trick is somewhat impractical.

"If you simply attack the other party's other theories and lower the other party's academic status...well, it's not impossible to do it, but this is just to attract hatred."

Wang Qi soon realized his huge advantage as a time traveler.

There is at least a half-century gap between the mathematics he studied and Chinese arithmetic. He doesn't even need to fully digest the other party's theory. He only needs to compare the other party's theory with what he has learned, and then find out the differences in details, and he can easily complete the task of "finding fault".

But this kind of destructive work rarely achieves academic prestige and can easily attract hatred. Wang Qi also hoped that the boss and Teacher Feng would stand in front of him and act as his T, so that he could accumulate enough food and slowly become the king.

As for total crushing... let's forget it. Suanjun is one of the strongest calculators in history, suspected to be No. 1. Comprehensive crushing is not only difficult, it is equivalent to having to independently deduce the mathematical system he has learned. According to Wang Qi's conservative estimate, once this work is completed, he will be happy.

After thinking about it for a while, Wang Qi sadly discovered that in fact, what he wanted to do basically remained the same. To do more would be to speed up the pace.

The gap between the two sides is really too big.

"However, it is precisely because of this that it is interesting!" Wang Qi stood up and stretched his body, then opened the door and walked towards the library at Shenjing's residence.

In addition to fighting spirit, there was pure brilliance in his eyes.

He has studied mathematics that far exceeds the existing system in China, so he knows that no matter whether he is the king or the master, whether he is the Li Zong or the Lian Zong, he will be completely defeated in this debate, and there will be no winner.

Gödel's incompleteness theorem will certainly shatter the perfect and optimistic dream of the master of mathematics, but in the future, the foundation of mathematics will still be recast by logic.

Therefore, in this debate, the temporary win or loss is not the point.

When competing with the greatest mathematicians in the world, what kind of glory can he achieve?

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In a place unknown to Wang Qi, a new storm is brewing.

Deep in the Wanfa Gate, the master of mathematics threw the monograph in his hand to the ground and laughed: "After so many years, it's still these twists and turns. Mr. Xi, are you planning to return to the ancient method these years?"

The master of mathematics Xi Boche was so angry that his face darkened even if he had done a good job in cultivating qi. Pang Jialai not only mocked them verbally, but just now, he directly expelled all the disciples around Xi Boche from the Wanxian Fantasy with his strong mathematical skills.

This is a naked declaration of war.

"Senior Pang is still as charming as ever - just like your vulgar paper."

"Haha." Pang Jialai laughed: "I came here this time for one thing."

Xi Boche didn't know what the other party was up to, and looked at him in confusion.

"I can't stay too long this time. But I can't let you blaspheme the way of calculation." Pang Jialai's eyes flashed: "So, let's make a bet?"

"What bet?"

"If I lose, I go back. If you lose, you go for me."

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Mr. Hilbert and Mr. Brouwer... This is really a tragedy. Mr. Brouwer has a hot temper and speaks without thinking. He was the first to use ginseng rooster. But after he accidentally scolded the entire German mathematics community, Mr. Hilbert, the good guy, finally got angry and united all the scholars working in Göttingen except Einstein to fuck each other. He had thought that Mr. Brouwer would soon regain his temper, and he could then be content to give up his supernatural powers. But Mr. Brouwer was too stubborn—he became sick with anger and accused Hilbert of having a brain problem… and then… and then…

This was truly a tragedy.