Into the Immortal Cultivation - Chapter 2088

[Chapter 101 Outbreak [Second Update]]

It was Feng Luoyi who fired the first shot for this world of great contention.

Although Ge Ting Zhai has been entrusted to He Weier, the first disciple of the master who is a cultivator of Lianzong, the Ge Ting faction is still orthodox from the sect, and it is still the direct line of the master. This will never simply change because of Hewel or any other personal factor.

Maybe a hundred years later, Ge Ting Zhai will eventually become another look, but He Weier alone cannot turn this stone around.

The core cultivator of the Ge Ting faction has already been stunned, and he is deliberately trying to equate Lian Zong’s rationale with the part of the division that was defeated by the ill-conceived calculations, and include them in the ill-conceived calculations. within the attack range.

But the first person to complete the results was Feng Luoyi, a genius known as “inhuman”.

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

They claim that the thinking that precedes set theory is flawed.

It should not start from “all”, but from “nothing”.

All “sets” must start from the “empty set” and build.

In other words, only sets built from the empty set are recognized as valid sets.

The other collections are all problematic, and they are all air lofts whose foundations have been removed by inconsiderate calculations.

Whether it is a finite set or an infinite set, it must start with the “empty set”.

The empty set corresponds to 0, {} corresponds to 1, and {, {}} corresponds to 2. If all sets, including infinite sets, are similarly well-ordered, then induction beyond infinity can be performed just like ordinary mathematical induction.

Then, all the axioms of the “Heavenly Li System” [Zf Axiom System], which is the highest achievement of Lizong, can be realized in the collection of good foundations.

This is Feng Luoyi’s proposition.

This genius completed this great argument with two papers successively.

Any proof construction must be of finite length, and proofs about contradictions are no exception. And the axiom of infinity, the axiom of existence of infinite sets of natural numbers, is applied to the successor operation and the empty set operation. These two operations have corresponding correspondences in Lianzong’s arithmetic. Therefore, these two arithmetics, between the Lianzong arithmetic and the Lizong arithmetic, are absolute. In other words, the Li Zong Arithmetic and the Lian Zong Arithmetic actually have a considerable degree of consistency.

This is the “absoluteness” of the two arithmetic.

Therefore, if there is a contradiction in the axiom of infinity, 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, monk Lian Zong vomited blood on a large scale.

Everyone knows that Lianzong, especially the Shaoli School represented by Lianzong in modern times, denied the “infinity” and the “law of excluded middle”. Jun Shun believes that there are no infinite objects in the material world, and there should be no infinite objects in the mathematical world.

This is to shake the foundation of Lianzong.

Countless Lianzong mathematicians scratched their ears and scratched their cheeks, wishing they could write a thesis immediately to counter Feng Luoyi.

However, Feng Luoyi’s second paper soon put an end to all the arguments.

“If the negative form of the axiom of infinity is taken as the axiom, the contradiction in the finite and good order will be more conveniently reflected on other axioms.”

“Therefore, in a sense, the axiom of infinity cannot be proved, nor can it be proved whether it is negative or not. .”

This time, it was like a thunderbolt from the blue, so that even Zonghuan was speechless.

Generally speaking, “falsifiability” is the foundation of the immortal way of today’s law. Something that is not falsifiable has no value for discussion.

However, the status of arithmetic is slightly special.

Even those mathematicians themselves can’t tell whether their work is “discovery” or “invention”.

On this point, Jun Jun and Wang Qi definitely hold completely opposite views.

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

Wang Qi also had this tendency after his encounter with the god of beauty.

He even stated in the preface of Formal Linguistics that this kind of debate is purely a chaotic natural language, and has to come up with two completely different concepts of “discovery” and “invention”.

But anyway, in the field of arithmetic, a theory that cannot be proved or falsifiable is allowed to exist.

But it is like theology, 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 the hell is there”.

But Feng Luoyi was just a coincidence. From the very beginning, he directly proved another point.

The axiom of infinity is safe.

“Not sure what’s in there”, but “safe”.

This also shows from the side that Lian Zong’s criticism of the concept of “infinity” is really meaningless.

And Chen Yujia’s paper was released shortly after.

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

Some people even cursed on the spot: “Traitor!”

Li Zong traitor!

In the past, almost all the monks took the basic faction as a matter of course. Wang Qi also clearly expressed his position on Lizong.

And now, Chen Youjia, a monk of Lizong, has published a paper with obvious Lianzong tendencies.

How can this make them not angry? How can you not be angry?

But more angry than them are the many grassroots disciples of Qianji Pavilion.

Type theory directly deletes Turing completeness and deletes loops.

Real Turing himself thought it was quite interesting, and even took it as a topic and left it.

But after the disciples of Qianji Pavilion discovered this, they immediately boiled over.

For them, it is inconceivable that there is no Turing-complete and loop-free calculator system.

They feel their sanctuary has been violated.

What used to be “free flying” is now “dancing in chains”.

Chen Yujia’s voice of “a traitor from the sect” also caused an uproar in Qianji Pavilion.

In this regard, Turing could only smile bitterly: “This is… it seems that I can’t help that girl.”

Feng Luoyi shook his head: “Let them make trouble. For these unreasonable guys , What role does that girl’s theory have, they will always know in the future.”

“Do you mean to incorporate ‘type theory’ into ‘Turing completeness’?” Turing real person smiled: “Vortex has been thinking about it these days. , 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 hexagram, he still trusts his disciples’ vision in this regard.

“I’m afraid that these two do not stick to each other, and I made a mistake at a critical time.” Turing was a little hesitant. The language associated with type theory, if there is a slight error, it will stop directly, which is considered safe. Although the methods used in the past would output unknown results, because the monks were already familiar with this field, they rarely dropped the chain at critical moments.

But if it is really a combination of the two…

what if the calculator crashes when the key is hit?

“If it’s the main magic weapon, it’s naturally another matter, but when it comes to cultivation, it does have an advantage.” Feng Luoyi said.

Real Turing suddenly smiled and said, “Brother Yuehan seems to have nothing to do with him now. Don’t you know? This wind of ‘Li Zong traitor’ has also blown on you, right?”

Feng Luoyi’s eyelids drooped: “They’re just stubborn people… they’re just old things that don’t change. Even if they didn’t see the truth clearly, they’re just like that.”

In fact, Feng Luoyi’s The thesis is not without opposition within Lizong.

In the beginning, it was because of the voice of the Qianji Pavilion cultivator’s objection to Chen Yujia that another voice of opposition was triggered.

Some Lizong cultivators felt that Feng Luoyi was crazy.

He actually got rid of the concept of “cycle”!

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

Therefore, such a thing as circulation should exist in arithmetic. In fact, it is even a key part of Wanfamen Gongfa.

“Circulation cannot be excluded from logic,”

said the Lizong cultivators.

Chen Youjia and Feng Luoyi both followed the “cutting one’s own finger” among the “two paths” of the master.

Even the two inspired each other to a certain extent.

But fundamentally, Feng Luoyi is the most orthodox Lizong, and Chen Youjia has accepted a lot of Lianzong’s ideas from Shunjun.

But they are pointing in the same direction.

Feng Luoyi never cared about such trivial matters. He said to Turing: “It’s enough that there is no opposition within the Gothing faction. Next, it’s up to them, right?”

Turing was noncommittal. Everyone knows that at this moment, the Ge Ting faction has already been put to death and then reborn.

Under the unscrupulous crushing, they couldn’t care less.

However, Real Turing did not expect that a few days later, the back-water attack of the Ge Ting faction would come so violently.

In fact, it was Feng Luoyi’s frequent transformation of Lianzong and Lizong’s arithmetic, which attracted their attention.

From this, they have extracted a function of an unnamed logical level.

“Double Negative Translation”. [It is called “Gödel-Genzen” translation on Earth]

“Assuming that there is a contradiction in the law of excluded middle, a negative proof of this hypothesis can be constructed.”

“And the law of excluded middle can be equivalent to the removal of double negation”.

These are two themes for which there is already plain proof.

At this time, the Gothing faction came up with a further idea.

“If a double negation is added to the proof in classical logic, can this proof be equivalent to the constructive proof of intuitionism?

” Elimination, then, is this thing equivalent to the constructive proof of the Shaoli School?

The answer is, “yes”.

It uses Lianzong’s Arithmetic against the Law of Excluded Middle to confirm that Lianzong’s opposition to the Law of Excluded Middle is also safe.

As safe as the axiom of infinity.

In other words…

Lianzong Arithmetic is no safer than Lizong Arithmetic.

[End of this Chapter]