Next, for half an hour, the audience was silent, only listening to Tan Ying's explanation, and only looking at Fan Hua's drawings.

The two have a wonderful tacit understanding, Tan Ying said wherever she said, and as soon as she turned around, she saw a picture that matched it.

He said that the density and discontinuity of rational numbers are a number axis in return.

He gave the example of an irrational number, and the back was an isosceles right triangle and a circle.

Unconsciously, a series of new concepts have also entered one by one.

Naming is undoubtedly a big problem.

For example, on the basis of the existing naming, the number previously defined by Wu Xiaozi is called "real number", and the infinite non-cyclic decimal number is called "fallacious number", which is undoubtedly very silky.

However, when imaginary numbers are introduced in the future, new troubles will be introduced.

After thinking about it, rational numbers and irrational numbers are more appropriate.

All rational numbers and irrational numbers also construct real numbers together.

Naturally, Tan Ying initially introduced the concept of sets and functions.

Needless to say, the name of the collection is just called the collection.

As for the function, Tan Ying followed the system of Fan Hua and named it "flow number", and the function curve was "flow line".

At this point, most people are already confused.

However, Fan nodded frequently when painting, feeling that Tan Ying thought more clearly than herself.

As a result, the situation eight years ago reappeared, and Tan Ying, just like Wu Xiaozi back then, unconsciously gradually became a solo lecturer for Fan Huashi.

This may be a common problem of teachers.

In this way, after the audience listened to this small stove for a long time, Tan Ying turned around in a daze and said: "What I said is quite simple, right, which one has a problem?" ”

Everyone bowed their heads blankly.

Can't.

Don't dare to have a problem.

Looking at their expressions, Tan Ying suddenly realized.

Wu Xiaozi is already myself.

Now, who else dares to question me, and who is qualified to question me?

It turned out that he was the loneliest.

When he met Fan Hua, it may be the greatest luck in his life.

And who will I meet?

Just as he was about to announce the completion of the sermon.

The only man who had followed the hall raised his hand reluctantly.

"Tan Ying, I don't agree."

This sound is like a cliff colliding, who is it not Fan Ya?

Tan Ying suddenly looked at her with a fierce look.

I don't want you, you go away!

But he didn't dare to say that, so he only dared to bow down humbly and say, "Si Ye, please." ”

Fan Ya then got up.

When it comes to doctrine, he is naturally more meticulous than anyone else.

At this moment, he put all the trivial matters of the day behind him, and only questioned as Tan Ying did when he was talking about it that day:

"Your definition of an irrational number is, infinitely non-cyclic decimals.

"I don't know if it's accurate, if it's proven, and I don't know how to express it mathematically.

"As you just said, Wu Xiaozi's biggest problem is that he blindly believes in intuition, axioms and models, and lacks pure mathematical and physical derivation and expression.

"But you're doing the same thing.

"You said that rational numbers and irrational numbers are combined to form all the numbers on the number line, so that the number line is continuous and complete.

How is this proven? Isn't there a third number on this axis? ”

Facing Fan Ya's questioning, Han Sun rubbed his head and Ying Li sighed.

At this time, there are still those who have more mental strength, and the only one is Fanzi.

However, some of the two applauded in unison.

Ying Yue: "Worthy of the fan!" Give me the Mo family to earn back the field! ”

Ji Qinghuang: "Wicked...... The wicked still need the wicked to grind! ”

Ying Yue: "Pay attention to what you say." ”

Xiaoqian: "Pay attention to what you say!" ”

Tan Ying's side, in the face of Fan Ya's undead angle lifting the bar, just as he was about to blurt out "This is not a matter of course".

He was suddenly stunned again, feeling more and more like Wu Xiaozi.

He said that rational numbers make up everything, beyond doubt.

I say that rational numbers and irrational numbers make up everything, and there is no doubt about it.

How am I different from him?

Yes, there is nothing to take for granted in mathematics, it is all proven and defined.

Suddenly, Fan Ya stepped forward: "With the help of the collection you just said, I have thought of a method, you might as well listen to it." ”

"Si Ye, please." Tan Ying respectfully stepped back.

Fan Ya asked for charcoal from Fan Huashi's hand, drew a shaft on the board, and drew a vertical line in the middle to divide it.

"Take this point as a cut.

"If the number line is outside this point, it contains all rational numbers.

This point is an irrational number.

"If it is expressed mathematically, according to the set theory you just mentioned, it should be like this......"

Fan Ya wrote as he spoke, combing his definition a little lamely against the set symbols of Tan Ying.

Between the hissing strokes of the pen, another small half of the board is gone.

Then he rubbed his cheeks again: "In this way, I can define the intersection of irrational numbers and rational numbers as a new set, which is what you call real numbers." Well...... If there is such a basis, I only need to prove that real numbers cannot be recuted, and that this number line is continuous, and these two will form the whole number line......"

After that, he frowned, and began to write to himself.

Just as he was struggling to write.

Tan Ying seemed to have heard something.

Airplanes...... Airplanes...... Airplanes......

When Fan Ya breathed a sigh of relief, he put his pen and looked back at Tan Ying, wanting to ask him "how".

only to find that the audience had risen solemnly.

Now.

He finally withdrew from the world of mathematics and heard the voice he had been looking forward to all his life.

Fan Ya slowly opened his mouth, like a child.

So that's it......

It turned out that what was in front of me was the same thing that was in front of me when I was painting......

The numbers are complete.

This axis is continuous.

The way is clear.

I am with the way of heaven.

It's an inch closer!

In the midst of that dingming, under the solemnity of the audience, Han Sun announced in a trembling voice:

"Please fan......

"Sit on the top.

"Asked."

……

As Fan Ya sat down and asked, it's hard to say anything else, Bai Pi, who is about to get off work, can't escape.

He didn't know why.

He's a porter.

In addition, it is only responsible for the maintenance of tripods that may not be used once for seven or eight years.

Fight a fight that you may not be able to fight in this life.

But how did all the work become his?

What's even more worrying is the old scholar in Fengtian.

Before this road is pointed, the giant is gone.

Then there is the Tao of Fan painting, they are all old ink people, and this material can't be left ungiven, right?

Now Fanzi, you also come here, and ask me to borrow materials, I gave it to my granddaughter, and I can't help but give it when I am a grandfather, right?

You are materialistic, and your Qin Palace has done me so much in one go.

How can you explain this to Fengtian......

Asked about the lobby, the banquet was extinguished.

Within ten years, Ding Ming twice, it can only be said that it is unprecedented.

is different from Tan Ying, Fan Zi sits on the top, and he deserves his name, everyone is really happy for him in their hearts, and it doesn't matter how many materials there are.

Tan Ying sat on the seat, watching Zhou Jingzhi replenish his protection, and there were unimaginable expectations in his heart.

Wu Xiaozi has a sentence that is true, mathematics is the foundation of all things.

As mathematics and physics cross this hurdle, more and more theories will surely be inspired by it and advance thousands of miles day by day.

The giant has fallen, but all things have been reborn.

Fan Huashi, Ying Yue and Fan Ya are just the beginning.

A new climax of the road-by-road era is coming.

It's forced to open, but it's still open.

In times like these, it is true that I as a materialist should no longer be restricted.

Thinking of this, Tan Ying couldn't help but say to the left and right: "Qian, when painting, we really have to step up our preaching." ”

Xiao Qianmeng nodded: "Master, I've been working hard." ”

Fan only stared at Fan Ya when he painted, and after meditating for a while, he suddenly asked for Xiao Qian's book and pen, and he bowed his head and wrote like Fan Ya.

After a while, she lit up the three lines of draft to Tan Ying: "This formula, can you set the limit?" ”

Tan Ying looked at those lines of expression, astringent and speechless.

Didn't you say that you should use your whole life to define it together, why are you like this?

But she's already like this, what can Tan Ying do.

He only gently pushed the booklet back, clicked on the few lines of definition, and said: "Mathematical systems are interconnected, and if you convert this collective expression into a flowing number expression, it will be the final appearance of that stone." ”

“！” Fan was stunned, "It's such a ......"

She then turned to look at Tan Ying: "You thought of it earlier?!" ”

"Hey~" Tan Ying grinned, "What is a teacher, it's better to teach people to fish than to teach them to fish." ”

"You can't look like a celebrity!" Fan gritted his teeth when he painted, and then he picked up the pen and sketched again, "Forget it...... Go back and train you again. ”

Next to him, Ying Yue looked stupid again.

I don't understand what they're talking about, let alone the relationship between them.

The words are lovers, the name is master and apprentice, and the senses are mother and son.

It's too complicated, I still don't understand.

Compared with the indescribable mathematics and ethics, he is more sensitive to specific things, and at this time he only suppressed his voice and said with Tan Ying: "The teacher has been in the Five Realms for many years, and today Wu Xiaozi has broken the Dao, and there is this opportunity to sit on the top, or he can go straight to the Six Realms." ”

"That's not a wonderful thing." Tan Ying nodded steadily.

"If that's the case, then only the teacher can be the next generation of giants."

"Wouldn't that be better?"

"It's wonderful, but the Mo family's headquarters and foundation are in Wangji." Ying Yue thought hard, "If the teacher really becomes a giant, he will be like Wu Xiaozi back then, I am afraid that he will go to Fengtian." ”

"Well, that can be changed." Tan Ying didn't worry at all, and only nodded at Han Sun, who was thinking differently on the other side, "You see, the sacrificial wine is already thinking about how to operate." ”

On the other side, Han Sun saw Tan Ying's expression from a distance, and also smiled with Ying Li beside him: "You see, Tan Ying is already thinking about how to move the Mo Family Headquarters to Xianjing." ”

"Ugh." Ying Li only sighed bitterly and bowed her head, "Teacher, don't be like this, I don't want to accept that Tan Ying is very similar to you." ”

"Isn't that glamorous?"

"......" Ying Li's expression suddenly tightened, "Teacher, not only is Tan Ying more and more like you, but you are also talking more and more like Tan Ying now." ”

“…………”

At this moment, Han Sun was finally a little scared.

He spends his days opening his teeth and blending into the jokes of the materialists......

Looking at it this way, isn't it me who is melting?

……

Unlike what was expected, Fan Ya's sitting on the top didn't take too long.

With only seven or eight pairs of materials, he was crumbling, but fortunately, Zhou Jingzhi held him steady.

After a few moments, Fan Ya came back to his senses.

I was dumbfounded, but speechless.

"Teacher......" Zhou Jingzhi asked in fright, "is this...... To be or not to be? Can you break through the six realms? ”

Fan Ya was short for a while when he heard this, and then suddenly put aside Zhou Jingzhi, and only walked quickly to the board, grasping the sides of the board with both hands and reading the lines of the line, chanting:

"It's a more important thing.

"There's something more important hidden here......

It is precisely because of this that Wu Xiao's paradox is also because of the confusion and difficulties in the academic world......

"How should it be described, how should it be described......"

In the end, he didn't feel like he looked at Tan Ying.

I don't know if it's because of his intuition, or because of the guidance of heaven.

He felt that Ayu was there.

Tan Ying has been immersed in the ink hall for many days, how can he be disappointed?

"Aximatization." Tan Ying said softly.

"Yes!" Fan Ya suddenly exhaled, turned around and said to everyone:

"Aximatization.

"Start with mathematics and science, and axiomatize all doctrines!

"It can be deduced as much as possible, it can be concise and concise as much as possible, and finally form an unbreakable system.

"That's my enlightenment."

"Remember, you must remember, this is the right way for all generations, with this foundation, the road is continuous, future generations can continue, follow this law, then the dispute can be settled, Dali can be determined!

"Alas! We have so much to do.

"Alas! Alack! If only I had been born......"

In the shock and incomprehension of the audience, only Han Sun opened his mouth and asked, "Si Ye has broken through the realm?" ”

"Breaking the realm? Oh, Break. Fan Ya thought for a while, and then spread his right hand, and there was no taste, "Compared with the eternal greatness of 'axiomatization', what is this realm?" ”

He had that said.

The weather on his body has also changed completely.

It's just not the shape you think.

It stands to reason that the breath of Fan Ya, the main soil and auxiliary gold, is meteorologically heavy and earthy, and it reveals inexplicable toughness, which has always been the most solid in the Qin Palace.

But at this time, the color of the earth was a little softened, and it softened a little.

In the eyes of ordinary scholars, this qi seems to be thin, not as good as before.

But led by Han Sun, the scholars above the three realms stood up in unison.

That's not thin.

Instead, between the earth and the king, something new has appeared......

Although visually he seems to be soft.

But if you look at it by qi, he is even stronger!

If you previously described Fan Ya with "diamond".

Now he is soft gold.

Although diamond is hard, there is always a moment of cracking and wearing.

Only real gold, although immortal.

Seeing this, Han Sun saluted first: "Congratulations to Fan Zi for breaking the realm!" ”

Everyone then rose: "Congratulations to Fan Zi for breaking the realm!" ”

Fan Ya was under the gaze of the full house, but he was also sluggish.

Am I changing?

Before I knew it, I had changed?

Such weather can only be ......

Thinking of this, he looked at Tan Ying with great trepidation and fear.

It is impossible to tell whether it is love or hate, whether it is to scold or hit.

You've even harmed me?!

For such a look, Tan Ying avoided it even more, and her face was sweating profusely.

Who the fuck is going to harm you......

It's not like you're going to give it for nothing......

Looking at such Fan Ya, even when Fan Hua, it was difficult to solve this problem, so he only shook his head secretly and said: "Grandpa is not easy to do now......

The only good news is that, just like the weather of the day, the people who noticed this tacitly did not break it.

In the treacherous atmosphere, it was Han Sun who made the final decision:

"Scrivener, remember.

"In the year 107 of the Word, the twentieth day of the seventh month.

Fan Zi sat on the top of the Qin Xue Palace and asked, breaking through the six realms, his qi is like real gold, or it is unique in the world.

Hearing this, everyone realized.

With Wu Xiao's broken road, there may not be a second person in front of Fan Zi.

This is not a giant, who can be called a giant?

It's just that they don't know.

Fan Ya has fallen into a paradox that belongs to him alone.

I may have to become a Mo giant......

But in fact...... The one who sat on the throne just now asked...... Under Tan Ying's final suggestion......

I have gradually taken on the form of a materialist......

As a giant of the Mo family, he preaches the Tao of materialism......

And so it goes...... With the advancement of axiomatization......

The future disciple of my Mo family...... It will also be dyed with the color of materialism......

Oops.

Am I the materialist?

Materialism with the knowledge of Mohists?

Cannot!

Only I can't be this giant!