There is an alchemist in a certain sect, and he once made a bold statement: "My alchemy skills are very superb and my reputation is full of China." I will alchemy for all those in the Immortal Dao who don't give themselves alchemy, and I will only give alchemy to these people!" There was an endless stream of people who came to him for alchemy, and naturally they were all those who couldn't make their own alchemy. However, one day, this alchemist felt that his cultivation had stagnated, and he instinctively opened the Dan furnace, so could he give himself alchemy?

This is the famous alchemist paradox, if it is replaced with the low version of the demonless plane, it is the alchemist paradox, if you want to express it loftyly, then it also has an equivalent expression - Russell's paradox.

Let the property P(x) denote that "x does not belong to x", it is assumed that a class a is determined by the property P - that is, "a=". First, if a belongs to a, then a is an element of a, then a has the property P, and from the property P knows that a does not belong to a, and secondly, if a does not belong to a, that is, a has the property P, and a is composed of all classes with the property P, so a belongs to a.

This is the conundrum that logicians cannot bypass: is the totality of a thing also a part of it?

This problem makes set theory inconsistent.

There are not no ways to circumvent this paradox, and Wang Qi knows two of them. The Zimmero-Frankl axiom system zF system and the von Neumann-Bonnes-Gödel nBg system. The former is a method of finite manipulation of sets, and the latter is the separation of sets from classes, which is the effort or struggle of earth mathematicians on this problem.

"If the set theory is not self-consistent for a day, the reckon will not admit defeat for a day - well, my admit, even if the set theory is self-consistent, it doesn't mean anything to him. Oh to him, it's an empty concept, a play on words. Wang Qi curled up in front of the study and read Shujun's paper again: "And to prove that the set theory is complete...... Am I stupid? I know that this road is incomplete when it goes to the dark, and I still want to prove this?"

Although this review paper by Shui Jun is more of a provocation and a kind of announcement, the author is one of the greatest economists in China after all, and there is still academic value.

For Wang Qi, the greatest value of this paper is still there, it sorts out the most critical problems currently encountered in Shenzhou's arithmetic logic.

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

With a small amount of logic, almost all arithmetic can be deduced - but in the eyes of the arithmetic, this is not arithmetic at all. In this case, no matter what Wang Qi does, he will be regarded as a "more funny trick" by the other party.

Well, on Earth, such polemics can easily descend into endless nitpicking, as well as personal attacks. Mathematics can't get through guò real yàn to throw out an irrefutable result, and the debate is basically torn up in the later stage. For example, historians of mathematics on Earth have unceremoniously accused both David Hilbert and Ruiz Brouwer of "lacking the character to confine the fight to the academic realm," which is the consequence of an overdose of ginseng rooster.

"In Shenzhou, everyone will probably do it in a more violent way, right?" For some reason, Wang Qi was faintly excited when he thought of the Wanfa Gate Battle.

In fact, the essence of this polemic is to increase the confidence of one's own people, and then find loopholes in the other theories of the other side, attack the other party's academic status, or do research similar to the other side, and prove that one's attainments in arithmetic comprehensively crush the other side, until one side has exhausted its confidence and can no longer resist the initiative to surrender, and then the other side will automatically win.

Of course, there is also a slightly shameless method in the academia of the earth - the young side waits for the old side to die of old age, and let time "prove it". It's just that in China, this kind of trick is a little impractical.

"If you simply attack the other party's other theories, you will lower the academic status of the other party...... Well, it's not that you can't do it, but it's all about pulling hatred. ”

Wang Qi soon realized his huge advantage as a traverser.

There is at least half a century between the mathematics he studied and the arithmetic of China. He doesn't even need to completely 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 the details, so that he can easily complete the task of "picking thorns".

But this kind of destructive work is difficult to achieve academic prestige and can easily attract hatred. Wang Qi also counted on the arithmetic master and Mr. Feng to be the T in front of him, and he would accumulate grain and become the king slowly.

As for the full crushing...... Forget it. Arithmetic Jun is one of the strongest arithmetic artists in history, and is suspected to be No.・1. It is not only difficult to fully crush it, but it is equivalent to deducing the mathematical system he has learned independently. According to Wang Qi's conservative estimate, when this work is done, he will be free.

After thinking about it for a while, Wang Qi sadly found that in fact, what he wanted to do had basically not changed, and doing more was to speed up his pace.

The gap between the two sides is simply too great.

"However, it is precisely because of this that it is interesting!" Wang Qi stood up and moved his body, then pushed open the door and walked towards the library of the Shenjing station.

In his eyes, in addition to the fighting spirit, there is more of pure brilliance.

He had studied mathematics far beyond the existing system of Shenzhou, so he knew that whether it was a monarch or a master, whether it was a detached sect or a relianzath, he would be defeated in this debate, and there would be no winner.

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

Therefore, in this debate, winning or losing for a moment is not the point.

When the world's greatest arithmetic is competing on the same stage, what kind of glory can you achieve?

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Unbeknownst to Wangsaki, a new storm is brewing.

In the depths of the Ten Thousand Methods Gate, Shujun threw the monograph in his hand on the ground and said with a smile: "After so many years, it is still these twists and turns-Mr. Xi, aren't you planning to cultivate back to the ancient law all these years?"

The master Xi Baiche was so angry that his face darkened even if he was in place. Pang Jialai not only mocked them verbally, but in fact, just now, he directly expelled all the disciples around Xi Baiche from the Ten Thousand Immortal Illusion Realm with his strong arithmetic skills.

This is a naked declaration of war.

"Senior Pang is still in style—just like your vulgar thesis. ”

"Huh. Pang Jialai smiled: "I came this time, in fact, just for one thing. ”

Xi Baiche didn't know what kind of medicine was sold in the other party's gourd, and looked at him suspiciously.

"I'm coming back this time, and I won't be staying long. But I can't let you blaspheme. Pang Jialai's eyes flashed: "So, let's make a bet, shall we?"

"Bet on what?"

"I lose, I'll go back. If you lose, you go for me. ”

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Mr. Hilbert and Mr. Brouwer...... It's a tragedy. Mr. Brouwer has a fiery temper and speaks without brains, and is the first to use ginseng cocks. But after he unintentionally scolded the entire German mathematical community, the good old man Mr. Hilbert finally went berserk and united all the scholars working in Göttingen except Einstein to attack each other. He had expected that Mr. Brouwer would soon resurge, and then he would be able to take it to his contentment. But Mr. Brouwer was too violent—he was angry, and accused Hilbert of having a bad brain...... And then...... And then......

It's a tragedy.