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

The two had a wonderful tacit understanding. When Tan Ying said that, she just turned around and saw a picture that matched her.

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

He gave an example of irrational numbers, and turned around to be an isosceles right-angle triangle and a circle.

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

Naming is undoubtedly a big problem.

For example, based on the existing naming, the number defined by Wu Shuzi before was called "real numbers", and the decimal number that is infinite and not cycled is called "fallacies", which is undoubtedly very smooth.

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

After thinking about it, it is more appropriate to have rational numbers and irrational numbers.

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

This is naturally here, Tan Ying initially introduced the concepts of sets and functions.

There is no need to say too much about the naming of a collection, just call it a collection.

As for the function, Tan Ying follows the system when painting, and named it "flow number", and the function curve is "flow line".

Speaking of this, most people are already confused.

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

So, the situation happened eight years ago again, and Tan Ying was like Wu Shuzi back then. Unconsciously, she gradually became a lecturer for the film painting alone.

This may be a common problem for teachers.

In this way, after listening to the small stove for a long time, Tan Ying turned around in a daze and said, "What I said is quite simple, right? Who has any questions?"

Everyone bowed their heads in a daze.

Don't dare.

Don't dare to have any problems.

Looking at their expressions, Tan Ying suddenly realized.

Wu Shuzi is already me.

Now that this is the case, who dares to question me and who is qualified to question me?

It turns out that he is the loneliest one.

When he meets Fan Hua, he may be his greatest luck in his life.

And who can I meet?

Just when he was about to announce the completion of the teaching.

The only man who followed this hall suddenly raised his hand.

"Tan Ying, I don't agree."

This sound is like a collision between a steep rock. Who is it if it is not Fan Ya?

Tan Ying suddenly had a fierce look.

I don't want you, go away!

But he didn't dare to say that, but he just bowed humbly and said, "Si Ye, please."

Fan Ya got up.

Once he talks about theory, he is naturally more meticulous than anyone else.

At this moment, he threw away all the trivial matters of today, just as Tan Ying asked when he made a clear talk on that day:

"Your definition of irrational numbers is that infinite does not cycle decimals.

"I don't know if this is accurate, if there is evidence, and I don't know how to express it in mathematical terms.

"You just said that Wu Shuzi's biggest problem is that he believes in intuition, axioms and model lakes, and lacks the derivation and expression of pure mathematics, physics and chemistry.

“But you are doing the same thing.

"You said that rational numbers and irrational numbers are combined together to form all the numbers on the number axis, and at this point the number axis is continuous and complete.

"How does this prove it? Isn't there a third number on this axis?"

Faced with Fan Ya's inquiry, Han Sun rubbed his head and Ying Li sighed.

At this time, only Fan Zi can compete with this.

However, the two of them both applauded.

Ying Yue: "I am worthy of Fan Zi! I will earn back the place with my Mo family!"

Si Qinghuang: "The wicked... the wicked still needs to be beaten by the wicked!"

Ying Yue: "Be careful when you speak."

Xiao Qian: "Be careful when you speak!"

On Tan Ying's side, facing Fan Ya's unblindly argument, just as he was about to blurt out that "this is not taken for granted."

He was suddenly stunned again, feeling that he was becoming more and more like Wu Shuzi.

He said that rational numbers constitute everything, and there is no doubt.

I said that rational numbers and irrational numbers constitute everything, but there is no doubt.

How is me different from him?

yes,

There is nothing to be taken for granted in mathematics, they are all proved and defined.

Suddenly, Fan Ya went in front of him: "With the help of the collection you just mentioned, I thought of a way, maybe I might as well listen."

"Siye asked." Tan Ying respectfully stepped back.

Fan Ya then asked for a charcoal pen from Fan Hua, drew a axis on the board, and a vertical line in it for division.

“Use this point as a cut.

"If the number axis outside this point contains all rational numbers.

"Then this point is an irrational number.

"If expressed in mathematical terms, according to the set theory you just mentioned, it should be like this..."

Fan Ya said and wrote, comparing Tan Ying's collection symbols, he sorted out his definition a little bit.

While hissing and writing, half of the board was gone.

Then he rubbed his cheeks directly: "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 this basis, I just need to prove that real numbers cannot be cut again, and this segment of number axis is continuous, and these two will construct the entire number axis..."

After saying that, he frowned and started writing on his own.

Just as he was writing hard.

Tan Ying seemed to hear something.

Buzz...buzz...buzz...buzz...

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

I realized that the audience had risen solemnly.

now.

He finally got out of the world of mathematics and physics and heard the sound he had been looking forward to for a lifetime.

Fan Ya slowly opened her mouth, like a child.

So that's it...

It turns out that what was blocking me was the same thing as what was blocking the painting...

The numbers are complete.

This axis is continuous.

The road was clear.

I and the way of heaven.

It's a little closer!

In the sound of the tripod, in the solemnity of the audience, Han Sun trembled and said:

"Please...

“Sit on the tripod.

"Ask."

...
To be continued...