Into the Immortal Cultivation

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It was Feng Luoyi who fired the first shot for this great battle.

Although Ge Ting Zhai has entrusted to He Waier, the first apprentice who is a monk of Lianzong, the Geting School is still an orthodox, still a master of the family. This has never changed simply because of factors such as Hewaier or any other person.

Perhaps a hundred years later, Ge Ting Zhai will eventually change to another way, but He Waier alone cannot reverse this stone.

The core monks of the Geting School have already killed their eyes, and they are deliberately going to equate even the separate calculations with the broken separation calculations that have been defeated by the bad calculations, and also include them in the bad calculations Within the scope of the attack.

But it was Feng Luoyi who was the first to complete the achievement-this genius figure known as "inhuman".

It should be said that Feng Luoyi found a new way of thinking.

They claim that there are problems with the ideas before set theory.

It should not start from "all", but from "none".

All "collections" must be constructed from the "empty set".

In other words, only the set constructed from the empty set is recognized as a legal set.

In addition to the collections, there are problems, and they are all air lofts whose foundations have been taken out of carelessness.

Whether it is a finite set or an infinite set, we must start from the "empty set".

The empty set ∅ corresponds to 0, {∅} corresponds to 1, and {∅, {∅}} corresponds to 2. If all sets, including infinite sets, have a similar well-ordered order, then it is possible to implement induction beyond infinity—just like ordinary mathematical induction.

Then, all the axioms of the "Tianli System" [ZF Axiom System], which is the highest achievement of Lizong, can be realized in a good foundation.

This is Feng Luoyi's proposition.

This genius used two papers to complete this great argument.

Any proof construction must be of finite length, and proofs of contradictions are no exception. The infinite axiom-the axiom of the infinite set of natural numbers, which is applied to the subsequent operations and empty set operations. These two operations have correspondences in the calculations of Lianzong. Therefore, these two arithmetics are absolute between consecutive and outlier arithmetics. In other words, there is a considerable degree of unanimous connotation between Lizong arithmetic and Lianzong arithmetic.

This is the "absoluteness" of the two arithmetics.

Therefore, if there is a contradiction in the infinite axiom, then this contradiction will also appear in the arithmetic through a "finite" translation process.

The infinite function axiom is safe.

As soon as this paper came out, it was the massive vomiting of blood by the monk Lian Zong.

Everyone knows that Lian Zong, especially the Shaoli, represented by Lian Zong in modern times, denies "infinity" and "exclusion law." Shujun believes that there are no endless objects in the material world, and there should also be no endless objects in the world of mathematics.

This is the foundation that has shaken Lianzong.

Countless consecutive statisticians scratch their heads and scratch their heads, wishing to write a paper immediately, and counterattack Feng Luoyi.

But, soon, Feng Luoyi's second paper made all the arguments subsided.

"If the negative form of the infinite axiom is taken as an axiom, the contradictions in the poor and good order will be more conveniently reflected in other axioms."

"Therefore, in a sense, the infinite axiom cannot be proved, nor can it be proved."

This time, it was like a thunderbolt on the sunny day, and all the sectarians in the town were speechless.

Generally speaking, "falsifiability" is the foundation of today's Faxian Dao. Things that do not have falsification have no value for discussion.

However, the status of mathematics is a little special.

Even the mathematicians themselves are not sure whether their work is "discovery" or "invention".

At this point, Shujun and Wang Qi absolutely hold opposite views.

Of course, at the level of the beauty god, this kind of contention is totally a joke.

Wang Qi also had this tendency after encountering Meishen.

He even stated in the preface of formal linguistics that this kind of argument is purely a chaos of natural language, and it is impossible to score two completely different concepts of "discovery" and "invention".

But in any case, in the field of mathematics, an unprovable and unfalsifiable theory is allowed.

But as if it were a theology, it is self-contained in its own logic.

Even if you want to destroy it, it is difficult to start.

For ordinary people, this is an unknown area of ​​"don't know what exactly".

But Feng Luoyi happened to be a coincidence. From the beginning, he directly proved another point.

Infinite axioms are safe.

"I don't know what's inside," but it's "safe."

This also illustrates from the side that Lian Zong's criticism of the concept of "infinity" is really meaningless.

Chen Youjia's thesis was also released immediately afterwards.

This time, it made all Lizong monks uncomfortable for a while.

Some people even scolded on the spot: "Traitor!"

Lizong traitor!

In the past, almost all monks took Kipai as a sect. Wang Qi also clearly expressed his stance from the sect.

Now, Chen Youjia, who is a monk of Lizong, has published a paper with a clear tendency to sect.

Why doesn't it make them angry? How can you not be angry?

But even more angry than them are the many grass-roots disciples in Qianji Pavilion.

Type theory directly deletes Turing completeness and deletes cycles.

Turing himself actually found it quite interesting, even leaving it as a topic.

But disciples of Qianji Pavilion immediately realized it.

For them, a computing system without Turing completeness and cycles is unthinkable.

They feel that their sanctuary has been violated.

What used to be "free flight" has now become "dancing with shackles."

Chen Youjia's "Li Zong traitor" 's voice was also tumultuous in Qianji Pavilion.

In this regard, Turing real man only had a wry smile: "This is ... it seems that I can't bear the girl."

Feng Luoyi shook his head: "Let them make trouble. For these uninformed guys, they will always know how the girl's theory works."

"Did you mean to include" type theory "in" Turing completeness "?" Turing smiled: "Vortex has thought about it in the past few days, and it may be vicious and discordant."

"But Wang Qi told me that this can greatly lower the threshold of arithmetic." Feng Luoyi said.

Thanks to the promotion of the Vientiane Gua Wen, he still trusts his disciples in this regard.

"I'm afraid that these two do not stick together. It's critical that something goes wrong." Turing was hesitant. The language associated with type theory, if there is a slight mistake, it will directly stop, which is safe. Although the methods used in the past will output unknown results, it is because the monks are already familiar with this field, so they rarely fall off the chain at critical moments.

But if it's really a combination of the two ...

What should I do if the calculator is down when it hits the key?

"If the main magic weapon is naturally different, but when practicing, it does have an advantage." Feng Luoyi said.

Turing real man suddenly smiled and said: "Brother Moon Han now is a matter of nothing to do with yourself. Don't you know? The wind of the" little traitor "also blows on you?"

Feng Luoyi's eyelids drooped: "It's just stubborn elements ... It's just an old thing that doesn't change. It doesn't even make them see the truth, so they do."

In fact, Feng Luoyi's paper is not without opposition within Lizong.

At first, it was because of the opposition of the monks of Qianji Pavilion against Chen Youjia that another voice of opposition was triggered.

Some Lizong monks felt that Feng Luoyi was crazy.

He actually eliminated the concept of "circulation"!

Circulation is a concept that exists widely in nature. The spiritual cycle represented by the breath of heaven and earth, the circulation of the atmosphere, and the circulation of water are all a kind of circulation.

Therefore, such a thing as circulation should be in the mathematics-in fact, it is even a key part of the Ten Thousand Falun Gong.

"Circulation cannot be removed from logic."

Those Lizong monks said so.

Both Chen Youjia and Feng Luoyi took the "two fingers" of the master's "two paths".

Even the two have inspired each other to some extent.

However, from the basic point of view, Feng Luoyi is the most orthodox divorce, and Chen Youjia has received many ideas from Lin Jun.

But they are pointing in the same direction.

Feng Luoyi never cared about this little thing. He said to Turing real people: "There is no opposition within the Geting School, it is enough. Next, it is up to them?"

Turing real people are noncommittal. Everyone knows that the Geting School is dead now and then born.

Under the ill-conceived crushing, they could not care much.

However, the real Turing did not expect that a few days later, the backing of the Geting School came so violently.

In fact, Feng Luoyi's means of frequently transforming the calculations of Lianzong and Lizong aroused their attention.

From this, they have refined a nameless logic level function.

"Double negative translation". [This is called "Gödel-Genzen" translation on Earth]

"Assuming that there is a contradiction in the law of exclusion, you can construct a negative proof of this hypothesis."

"While the law of exclusion is equivalent to the removal of double negation."

These are two topics that already have obvious proofs.

And at this time, Geting sent forward a further idea.

"If double negation is added to the proof in classical logic, is this proof equivalent to the constructive proof of intuitionism?"

That is to say, if the part that belongs to the "exclusion law" in the Geting School's algorithm is eliminated, then, is this thing equivalent to the structural proof of Shaoli?

The answer is "yes".

It uses the Lianzong arithmetic against the law of exclusion to determine that the law of exclusion from the law is also safe.

As safe as the infinite axiom.

In other words ...

Lian case arithmetic is no safer than leaving case arithmetic.

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