"If α is an irrational number, then any μ∈ [0,1] is a gathering point of the sequence {nα-[nα]}, where [x] denotes the integer function. ”

This is an inference that is easy to prove.

It's simple, but it's practical.

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

“...... Consider using the counterproof method to set 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 equation......"

“...... This means that 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 positive infinity satisfies x0+mkμ-[x0+mkμ]→0(k→+∞). ”

"Therefore, we can get L=limn→+∞f([x0+mkμ])=limn→+∞f([x0+mkμ]-x0-mkμ+x0)=f(x0)......"

Based on the above, it can be deduced 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 inversion is overturned, and the proposition is proved. ”

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

No errors were detected.

Chen Zhou was ready to hand in the papers.

However, he glanced at the scratch paper, which was still blank.

After thinking about it, Chen Zhou wrote his name.

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

The first course of the midterm exam season, the number of points is 1.

The classmate sitting behind Chen Zhou was still immersed in solving the problem, and suddenly looked up and found that Chen Zhouren was gone.

The classmate looked around again, and it was indeed only Chen Zhou who was gone.

He muttered to himself, "Aren't you so nervous that you're short of breath?

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

Turn on the computer, take out the scratch paper and pen, pick up the thoughts before the exam, and continue working on the project.

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

Start with the helicopter facing or facing away from the satellite, taking into account the elevation angle of the satellite.

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

Combined with geometry and other mathematical methods, various parameters of rotor communication are comprehensively analyzed.

Thinking of this, Chen Zhou's train of thought was completely opened.

He no longer sticks to the surface of the subject.

Instead, it combines the characteristics of different mathematics courses and comprehensively uses mathematical methods to solve this problem.

About half an hour later, Zhao Qiqi and the three 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 out of line?"

Chen Zhou thought for a while and said, "It's not super outline, right..."

Zhao Qiqi and the three of them looked at each other, and Li Li asked out loud: "Chen Zhou, the last question is the content of counting 2 points?"

Chen Zhou turned his head and glanced at Li Li, and nodded slightly: "Sort of, I used a corollary of Dirichlet's approximation theorem in number theory to solve it." This theorem is also found in the number 2, a result of the point-by-point convergence of the Fourier series. ”

Hearing Chen Zhou's words, Li Li said: "I also think of this theorem, but this part of the content is at the end of the number 2, I haven't fully grasped it, and I don't know the inference you said..."

Zhao Qiqi and Zhu Mingli were thoughtful...

Chen Zhou turned to say: "The dispute between the subject of Professor Wu's engagement, every time it is an over-the-top topic, you should get used to it." And this is only the last chapter of the number 2, which cannot be regarded as a super-outline question. ”

Zhao Qiqi: "Then why are you talking about a corollary of the theorem of number theory?"

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

Zhao Qiqi: "......"

Zhu Mingli: "......"

Li Li silently walked to the desk and sat down, and took out the textbook that counted 2.

After the exam, Huang Yemei took the collected test paper and came to Wu Xiping's office.

Pushing open the door, Huang Yemei said, "Professor Wu, I didn't expect that your test papers and classmates could submit them in advance, and I don't know how to do it." ”

Wu Xiping was lying on the desk writing materials, and said without raising his head: "Just Chen Zhou alone, right?"

Huang Yemei asked with a little surprise, "How do you know?"

Wu Xiping replied: "At present, except for him, no one can completely make 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, still don't care enough about the students of our mathematics department." ”

Huang Yemei was slightly stunned, she didn't understand what Wu Xiping meant, she said, "Nothing has happened to the freshmen in the mathematics department recently." In the first two months of school, I have been to all the students' dormitories, and they are all very good. ”

Wu Xiping asked, "Then when you went to Chen Zhou's dormitory, you didn't find anything different?"

Huang Yemei thought for a moment and replied, "Hmm... When I went, Chen Zhou was not there. According to other students, it seems that they went to the library to read a book. ”

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

It was not long after the start of school that she went to Chen Zhou's dormitory.

When she saw 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, she realized that something was wrong, and she took away the books not long ago, and there were two of them with handwriting?

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

7 big questions, neat handwriting, clear thinking, and correct answers.

Wu Xiping took out a red pen, brushed and brushed 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, glanced at it, and immediately looked up at Wu Xiping.

Wu Xiping smiled: "This kid is expected. ”

Huang Yemei heard a trace of appreciation from Wu Xiping's tone.

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

Wu Xiping's several-score test papers, the students were all complaining bitterly, either exceeding the outline or exceeding the outline.

Some students even chose to drop their points and choose to retake the course.

This is the first time she has heard Wu Xiping praise a student unabashedly.

"By the way, if the undergraduates of our school apply for the subject separately, are there any requirements?" Wu Xiping usually has a subject in addition to substitute teaching, and he understands the school's regulations in this regard, but he is not familiar with it.

Huang Yemei asked suspiciously, "Undergraduate, is it Shen Jing that you have been carrying?"

Shen Jing, a student, Huang Yemei still knows, since his sophomore year, he has been following Wu Xiping to do projects.

Now that Shen Jing is in his third year, if he is good enough, he can indeed apply for the subject independently, but according to the school's regulations, it is still difficult and difficult.

Wu Xiping nodded first, and then shook his head: "It's Shen Jing and Chen Zhou." ”

Huang Yemei was slightly stunned, how could it be Chen Zhou again, even if he scored a full score in the exam, he wouldn't be able to apply for a topic, right? Isn't this a freshman who has just been enrolled for two months?