"If α is an irrational number, then any μ∈[0,1] is the clustering point of the sequence {nα-[nα]}, where [x] represents the rounding function."

This is an easy-to-proof inference.

Although simple, it is practical.

As a result, Chen Zhou's ideas have been opened and he began to write and answer the last question.

"... Consider using the reverse proof method and counter-suppose limn→∞f(n)=L, because μ is an irrational number..."

"...... there will be f([nkμ])=f([nkμ]-nkμ), consider the limit of k→∞ for this formula..."

“……this means L=limn→∞f([nkμ])=limn→∞f([nkμ]-nkμ)=f(0)....”

"...... Then take any real number x0, and there is a positive integer sequence {mk} that tends to be positive infinite satisfies x0mkμ-[x0mkμ]→0(k→∞)."

"Therefore, we can obtain L=limn→∞f([x0mkμ])=limn→∞f([x0mkμ]-x0-mkμx0)=f(x0)....."

"In light of the above content, we can infer that (?x)f(x)≡f(0), but the continuous identity function defined on the real axis does not have a minimum positive period, so the counter-assumption is overturned and the proposition is proved."

After writing, Chen Zhou looked back and read it again.

No error was checked.

Chen Zhou was about to hand over the papers.

However, he looked at the draft paper and it was still blank.

After thinking about it, Chen Zhou wrote his name on it.

Then, get up, hand in the papers, and leave.

The first exam in the midterm exam season, with a score of 1.

The classmate sitting behind Chen Zhou was still working hard to solve the problem. Suddenly, he looked up and found that Chen Zhou was gone.

The classmate looked around again and found that Chen Zhou was the only one who disappeared.

He murmured to himself: "Aren't you so nervous that you're short of breath? Can you hand in the paper in advance?"

After leaving the classroom, Chen Zhou went straight back to the dormitory.

Turn on the computer, take out the draft paper and pen, follow up the thoughts before the exam, and continue working on the topic.

Like Shen Jing's work, the part Chen Zhou is responsible for also needs to be analyzed on and off.

Starting from the direction of the helicopter towards or backward toward the satellite, consider the elevation angle of the satellite.

This topic is actually a simulation experiment, using mathematical analysis as a tool.

Combining mathematical methods such as geometry, comprehensively analyze various parameters of rotor communication.

Thinking of this, Chen Zhou completely relaxed his ideas.

He no longer sticks to the surface of the subject.

Instead, we combine the characteristics of different mathematics courses and comprehensively use mathematical methods to solve this problem.

About half an hour later, Zhao Qiqi and the other two returned to the dormitory together.

As soon as he entered the dormitory door, Zhao Qiqi asked, "Brother Chen, how did you solve the last question? Is it beyond the outline?"

Chen Zhou thought for a while and said, "It's not beyond the rules..."

Zhao Qiqi and the other two looked at each other, and Li Li asked, "Chen Zhou, is the last question the content of the 2?"

Chen Zhou turned his head and looked at Li Li, nodded slightly: "That's right, I used a deduction of Dirichlet's approximation theorem in number theory to solve it. This theorem is also found in number 2, about Fourier

A result of series convergence point by point."

Hearing Chen Zhou's words, Li Li said: "I thought of this theorem, but I haven't fully grasped this part of the content at the end of the 2nd, and I don't know what you said..."

Zhao Qiqi and Zhu Mingli thought about something...

Chen Zhou turned around and said, "Professor Wu's dispute over the subject matter is always beyond the syllabus. You should be used to it. And it has only exceeded the last chapter of the number 2, and it cannot be considered beyond the syllabus."

Zhao Qiqi: "Then why do you say a reason for the number theory theorem?"

Chen Zhou: "It's all the same, the same."

Zhao Qiqi: "..."

Zhu Mingli: "..."

Li Li Mo walked to the desk without saying a word and sat down, taking out the textbook for 2 points.

After the exam, Huang Yemei came to Wu Xiping's office with the collected test papers.

When he opened the door, Huang Yemei said, "Professor Wu, I didn't expect that some classmates would be able to hand in the papers you gave in advance, and I don't know how it was done."

Wu Xiping was lying on the desk writing materials, and said without raising his head, "Is Chen Zhou the only one?"

Huang Yemei asked in surprise: "How did you know?"

Wu Xiping replied: "At present, no one except him can fully produce this test paper."

After a pause, Wu Xiping put down the pen in his hand, raised his head and said with a smile: "It seems that you, the counselor, don't care enough about our mathematics students."

Huang Yemei was slightly stunned and did not understand what Wu Xiping meant. She said: "Nothing happened to the freshmen in the mathematics department recently. In the two months since the start of school, I have been to all the students' dormitories, and they are all pretty good.

”

Wu Xiping asked, "Then you didn't find any difference when you went to Chen Zhou and his dormitory?"

Huang Yemei thought for a while and replied, "Well... Chen Zhou was not here when he went there. According to other classmates, it seemed that he was going to the library to read books."

Suddenly, Huang Yemei thought of the stack of textbooks that Chen Zhou took away from her at the beginning of school.

It wasn't long before school started, she went to Chen Zhou's dormitory.

Seeing the pile of textbooks, she flipped through them casually, and only one or two of them had handwriting, so she didn't care.

Now that she thought about it carefully, she found something wrong, and she took two books that had been away for a while, and there were two books with handwriting? Did she finish reading it or just draw it casually?

Wu Xiping took the test papers for this exam, found Chen Zhou's, and read it.

7 major questions, the inscriptions of answers are neat, the ideas are clear, and the answers are all correct.

Wu Xiping took out a red pen, ticked it a few times, and wrote down a big red number "101".

Then, hand the test paper to Huang Yemei.

Huang Yemei took the test paper, took a look, and immediately looked up at Wu Xiping.

Wu Xiping smiled and said, "This kid is expected."

Huang Yemei actually heard a hint of praise from Wu Xiping's tone.

Although she has not been a counselor in the mathematics department for a long time, she has also heard of Wu Xiping's name.

The students complained about the number-point test papers produced by Wu Xiping, either beyond the syllabus or beyond the syllabus.

Some students even chose to lose a few points and choose to retake the exam.

This was the first time she heard Wu Xiping and praised a student without any concealment.

"By the way, if undergraduates in our school apply for a separate project, do you have any requirements?" Wu Xiping usually has a substitute class, but is not familiar with the school's regulations on this aspect.

Huang Yemei asked in confusion: "Undergraduate? Is it Chen Jing you have always carried?"

Huang Yemei still knows Chen Jing, a student, and has been working on projects with Wu Xiping since his sophomore year.

Now Chen Jing is in his junior year. If he is excellent enough, he can indeed apply for a project independently, but according to the school's regulations, it is still difficult and difficult.

Wu Xiping nodded first, then shook his head: "It's Chen Jing and Chen Zhou."
Chapter completed!