Xueba, I beg you to go and escort him quickly!

Page 494

"Here, the method of Cauchy sequence is used to construct real numbers from rational numbers. Let C represent the set of Cauchy sequences of all rational numbers. Then the real number R we want to construct is the quotient of C divided by an equivalence relationship:"

Xu Heng wrote:

R:=C/~

"This equivalence relationship..."

"..."

"Later we will define the true limit and prove that the formal limit of a Cauchy sequence is the same as the limit of this sequence."

"The reason for defining formal limits is to avoid circular arguments: Defining the real numbers requires the concept of limits, and the concept of limits can only be properly defined once we have defined the real numbers."

"So far, the real numbers are defined."

"And then the decimal representation of the real numbers..."

"..."

"The proof is mainly based on the Archimedean property of the real numbers."

"Finally show an example that the decimal representation of real numbers is not unique."

"..."

Xu Heng considered all aspects.

"The number 1 has only these two decimal representations."

"In fact, all real numbers, when it is a finite decimal, that is, a number that is all zeros from a certain digit after the decimal point, it has two decimal representations, and when it cannot be represented as a finite decimal, it has only one decimal representation .”

finished!

Done!

put down the pen!

Xu Heng breathed a sigh of relief.

Not only the students were stunned, but also Luo Yingnan and the math teachers.

They froze!

The students don't understand very well!

Luo Yingnan and the others actually did too!

She's already talking fast enough!

But Xu Heng was faster than him!

!!!

"Student Xu Heng, what do you think of us!"

"You're too fast!"

"Hiss... we didn't keep up with our train of thought!"

Several teachers blushed.

Xu Heng, "Uh..."

"Teacher, you did it on purpose! It's just that their thinking can't keep up, and you can't keep up either?"

"Have I spoken slowly enough?"

All the teachers instantly had blue veins on their foreheads.

"Pfft..."

"Student Xu Heng! You are pissing me off!"

"Student Xu Heng, why don't you order something from the Yangjian!"

"Slow enough?"

"You're trying to be annoying, aren't you!"

"Student Xu Heng, please, don't do this! Really don't do this! Please!"

"Don't pull me, I'm going to fight him!"

"!!!"

Xu Heng sighed when he saw the reaction of these teachers.

"Hey……"

He knew he seemed to have said something wrong.

I am too high profile!

but--

He really spoke slowly enough.

He thought that these teachers could understand faster on the basis of the original, it seems that he was thinking too much.

Turning his head, Xu Heng looked at Yue Pingting.

Yue Pingting was startled, she was terrified, "???"

"Huh?... What's wrong? Xu Heng...why are you looking at me like this?...I don't understand! I don't know...don't look at me like that!"

"These teachers don't understand, how can I understand!"

Xu Heng, "%￥#@￥%..."

The group of teachers waited for a while before calming down.

"hiss……!"

"call……!"

Take a deep breath, take a deep breath, calm down, calm down!

But there was still a teacher who couldn't bear it, turned around and went to the corridor, he couldn't calm down at all.

Luo Yingnan stared at Xu Heng with fiery eyes.

"Student Xu Heng..."

Xu Heng pouted, "Teacher Luo, please tell me?"

Luo Yingnan, "I have an unfeeling request... I wonder if you can agree."

"Seeing that the class will start soon, can you please move to the conference room and give us another lecture?"

"It won't take much of your time! Can it work?"

Xu Heng took out his phone and checked the time...

Luo Yingnan, "Of course, if you are willing and free, can you?"

"Don't worry, we will discuss it with the teacher of the next class as soon as possible..."

Xu Heng smiled, "No, let's go!"

Luo Yingnan was stunned, "But...the teacher in the next class...this...?"

Yue Pingting smiled and said, "Teacher, it's okay. All the teachers are used to Xu Heng like this, so it's okay."

are used to...

I go!

Come anytime, go anytime!

Ma'am, too, it's convenient!

"Ring Ling Ling..."

As the class bell rang, Xu Heng left, taking Wu Yingnan and the others with him.

At the same time, the teachers who were supposed to attend the class also turned back.

The chemistry teacher who came to class was stunned.

Didn't you agree to attend the class?

Why is there no one?

???

Nima!

You are going too far!

There were so many people in the morning, and they couldn't stand behind. Fortunately, there was no one there.

You don't take me seriously!

It hurts so much!

PS: New month!Begging for a monthly pass!Ask for a monthly pass!Ask for a monthly pass!Woo hoo!Kneel down! .

Chapter 299

conference room.

Twenty or thirty teachers surrounded Xu Heng.

Although there are seats, some of them are still standing.

Because standing behind Xu Heng is far more able to express their inner excitement than sitting opposite Xu Heng.

Luo Yingnan found a pen and paper, "Student Xu Heng, I'm tired of you."

Xu Heng nodded slightly, neither happy nor angry.

As for the other teachers, you look at me one by one, and I look at you.

"What's going on here?"

A teacher replied, "Student Xu Heng is proving that the cycle is equal to 1!"

"Ms. Luo and the others made mistakes in their proof before, and Xu Heng pointed it out. There are many things they don't understand, so I want to ask Xu Heng."

"Hiss...so that's how it is..."

"and many more!"

"what's the situation?"

"What you said just now is...yes! Hiss...I'll go! Student Xu Heng give Teacher Luo and the others proof?"

"Pointed out a few teachers' mistakes?"

"This this……"

A teacher boldly admitted, "Yes! We discussed it for half a month before, but Xu Heng directly pointed out the mistake!"

"I don't want to admit it, but it's the truth."

"Hey……"

"Xu Heng's proof seems to be correct!"

"His proof is not something superficial, but a strict proof!"

"hiss……!"