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

Page 492

"If I were Xu Heng, how wonderful it would be! I'm handsome! I'm capable!"

"Dream more!"

"Bah! I can't even dream of it! Hey! Hey!! Hey!!!"

"%￥#@#￥%..."

"..."

Xu Heng, "Let's calculate the difference between these two numbers. In fact, we will find that subtracting the two numbers seems to be unable to find a reasonable number to express the difference."

Yue Pingting still didn't give up, "Infinitesimal! It should be infinitesimal!"

Xu Heng, "The infinitesimal means that it is infinitely close to 0, right? But the infinitesimal cannot find a corresponding position on the number axis to express it."

Yue Pingting asked, "Why?"

There were more and more doubts in her head.

Xu Heng looked at Yue Pingting who refused to give up, and continued to ask, "Is the infinitesimal constant or variable?"

Yue Pingting, "Constant! That is, a fixed quantity!"

Feng Nianchang knew that, for example, 1 is a constant, 2 is also a constant, every point on the number line is a constant, and real numbers are constants, right?

What is a variable?

It is a number that is constantly changing.

Xu Heng, "Are you sure? But you clearly said before, infinitesimal."

"The infinitesimal is actually a variable, because it is infinitely approaching 0, and it has never stopped close to 0."

"So if the difference between 1 and the cycle is defined as infinitesimal, and the infinitesimal is a variable, it is obviously still impossible to explain whether 1 and the cycle are equal."

Yue Pingting put on a bitter face, "Ah? What and what! I still don't understand!"

"Am I too stupid?"

"Or Xu Heng, your statement is not convincing?"

Feng Nianchang interjected, "Or, is there any simple way to prove it?"

Xu Heng, "You all know that 0.2222+0.3333=0.5555, right?"

Feng Nianshang and Yue Pingting nodded.

Xu Heng, "When adding two decimals, each digit of the decimal point is added separately. This is very simple and needs no further explanation."

“那么我们同时也知道1/3=0.3333循环，并且1/3+1/3+1/3=1，所以我们可以得出结论：0.3333循环+0.3333循环+0.3333循环=1。”

"It's not wrong, is it?"

Feng Nianshang and Yue Pingting were stunned for a moment.

Xu Heng, "According to the rules we just added for decimal points, the addition of decimal points is actually the addition of the respective decimal places alone, so the conclusion is: 0.3333 cycles + 0.3333 cycles + 0.3333 cycles = 9 cycles."

"So to conclude: 1 = 9 cycles."

Yue Pingting, "Yes, yes..."

She wanted to refute, but for a moment she didn't know what to say.

Xu Heng, "The above proof process is actually relatively rough, but it is still a way of proof. In fact, there are already more scientific proof methods."

"Let me tell you another way of thinking. In fact, there are many ways of thinking about such a proof."

"I'll try not to say what you don't understand."

"The above is the first type, so let's talk about the second type now. Let a=9 cycles, then 10a is 9.9999 cycles, so 9a=10a-a=9.999 cycles-9 cycles=9, so a=1."

Yue Pingting couldn't believe what she heard, she opened her mouth slightly.

But Xu Heng hasn't finished yet, "The third type, 9 cycles can be regarded as a geometric sequence whose first term is 0.9 and the total ratio is 0.1, a1=0.9, a2=0.09, a3=0.009, and so on, all The sum of the terms...According to the summation formula of the geometric sequence, it can be obtained that the 9 cycle is equal to 0.9+0.09+0.009+a1 divided by 1 minus q, that is, 0.9 divided by 1 minus 0.1, so it is equal to 1. "

Yue Pingting's mouth opened even wider...

Because Xu Heng has three ways of proof at his fingertips!

What surprised her even more was that she couldn't refute this seemingly simple idea.

Yue Pingting was taken aback for a while.

Xu Heng, "Of course, the above three ideas are just to help you understand intuitively, and you can't take this as a strict proof."

Feng Nianshang and Yue Pingting said in unison, "Why?"

Xu Heng, "The strict representation of infinite decimals like cycles is beyond the scope of elementary mathematics. You can't take it for granted to do ordinary addition, subtraction, multiplication, and division operations on infinite decimals like cycles, so the above three elementary ideas can only be considered opportunistic. Elementary understanding, not strict proof."

These two are curious!

Feng Nianchang has always wanted to know how to prove it.

Yue Pingting was not convinced!

"I just think these three proofs are too hasty to convince me."

Xu Heng, "Then wait until I finish eating."

"Uh-huh!"

There are two girls, one is more like Yujie, and the other is more like cute.

The two stared at Xu Heng intently.

Really envy others!

After Xu Heng finished eating, he got up, and they also got up.

Xu Heng walked out, and they followed suit.

"Uh... I'm going to the toilet, you guys wait..."

Feng Nianshang and Yue Pingting's faces turned red instantly.

"%￥#@￥￥%..."

They were not far from the men's toilet, waiting for Xu Heng.

This makes many boys, "???"

"what happened?"

When Xu Heng came out, they went up to meet him.

All the boys said, "I'm damn! I'm dying of thirst, I'm dying of thirst, I'm dying of water!"

Xu Heng ignored these people and talked while walking.

"The way modern mathematics defines the equality of two real numbers is that the Cauchy sequences corresponding to the two real numbers converge to the same limit."

"Cauchy sequences corresponding to cycles and 1 converge to the same limit."

"So these are two different representations of a real number."

"A phenomenon produced by the decimal notation itself."

Yue Pingting, "???"

Feng Nianchang, "???"

They don't understand!

Xu Heng, "It's not clear what you say, go to class! Anyway, it's break time now."

But when the three appeared in the class, the mathematics teachers who were attending the class did not go to rest, but waited for Xu Heng outside the classroom.

Xu Heng, "Uh..."

Several teachers headed by Luo Yingnan were delighted when they saw Xu Heng came back.

"Student Xu Heng, you are back!"

Xu Heng, "Hello teachers, are you...?"

Luo Yingnan and the others smiled at Xu Heng, "I'm really sorry Xu Heng, I read your chat history with Mr. Hong before, I'm sorry, I hope you forgive me..."

Xu Heng, "It's okay, I also know that you have seen it in 0.4, and there is nothing shameful about it."

Xu Heng doesn't care if he doesn't care, but they have to show their attitude.

Luo Yingnan, "Also... about the two questions you and Hong Lao were discussing."

It was because of this!

In other words, they just wanted to know more about Xu Heng's excellence in mathematics.

Why did Xu Heng do this?

Wait, a series of related questions.

Thinking of this, Xu Heng felt a little headache.

"Sorry, teachers, the three of us still have some things to do."

Luo Yingnan, "Is... what is it?"

Feng Nianshang, "Proof that the cycle is equal to 1."

"We know this! Several of our teachers have proved it together before!"

Luo Yingnan and the math teachers looked at each other and laughed.

Yue Pingting immediately said, "Teachers, it's not the kind of one-third and other superficial proofs, but real proofs! There must be strict proofs with reasons!"

Luo Yingnan and several teachers nodded, "Yes, it is a strict proof!"

"Student Xu Heng, you three have made trouble here! It's okay, the few of us have studied this rigorous proof together..."

After speaking, they borrowed the stool from the classmate next to them and sat down, then picked up the pen and paper and prepared to write.

The other teachers also looked at each other and smiled, "It turns out that student Xu Heng is sometimes difficult to come by! Huh..."

Yue Pingting froze for a moment, "No no no! Teacher, you seem to have misunderstood something."

……

PS: Thanks to [Mobai] [xing] [tail number 3571] [Dream Stealer] for their support!

It's February!New January!I wish you a fortune!Good luck! .

Chapter 298

Misunderstand?

Misunderstood something?

After Luo Yingnan and several teachers exchanged glances, they finally locked their eyes on Yue Pingting.