Xueba starts with change

Chapter 121 After handing in the paper
"If α is an irrational number, any μ ∈ [0, 1] is an accumulation point of the sequence {nα-[nα]}, where [x] represents the rounding function."

This is an easily proven inference.

Although simple, it is practical.

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

".Consider using the method of proof by contradiction, anti-set limn→+∞f(n)=L, because μ is an irrational number."

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

".That is to say L=limn→+∞f([nkμ])=limn→+∞f([nkμ]-nkμ)=f(0)'

".Take any real number x0 again, there exists a sequence {mk} of positive integers tending to positive infinity satisfying x0+mkμ-[x0+mkμ]→0(k→+∞)."

“故可以得到L=limn→+∞f([x0+mkμ])=limn→+∞f([x0+mkμ]-x0-mkμ+x0)=f(x0)”

"Synthesizing the above content, it can be deduced that (x)f(x)≡f(0), but the continuous identity function defined on the real axis has no minimum positive period, so the antithesis is overthrown, and the proposition is proved."

After finishing writing, Chen Zhou went back and stroked it again.

No errors were detected.

Chen Zhou was ready to hand in the paper.

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

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

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

The first door of the midterm exam season ends with a score of 1.

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

The classmate looked around again, and it was true that only Chen Zhou was gone.

He murmured to himself: "Isn't he so nervous that he has shortness of breath? This can also be handed in 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, pick up the thoughts before the exam, and continue to work on the project.

Like Shen Jing's work, the part Chen Zhou is in charge of also needs to carry out on-off analysis.

Starting with the direction the helicopter is facing or away from the satellite, consider the satellite's elevation angle.

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

Combined with mathematical methods such as geometry, various parameters of rotor communication are comprehensively analyzed.

Thinking of this, Chen Zhou completely let go of his thoughts.

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, the three of Zhao Qiqi returned to the dormitory together.

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

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

The three of Zhao Qiqi looked at each other, and Li Li asked aloud: "Chen Zhou, is the last question about counting 2?"

Chen Zhou turned his head to look at Li Li, and nodded lightly: "Well, I used a deduction of Dirichlet's approximation theorem in number theory to solve it. This theorem is also included in Divide 2, about Fourier A result of the point-by-point convergence of the series."

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

Zhao Qiqi and Zhu Mingli were thoughtful.
Chen Zhou turned to say: "Professor Wu's dispute over the subject is always over the outline, you should get used to it. And this is only a few points beyond the last chapter, so it can't be considered over the outline."

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

Chen Zhou: "They are all connected, the same."

Zhao Qiqi: "."

Zhu Mingli: "."

Li Li went to the desk and sat down without making a sound, and took out the textbook with a score of 2.

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

Pushing open the door, Huang Yemei said, "Professor Wu, I didn't expect that some of your test papers would be handed in ahead of time, and I don't know how you did."

Wu Xiping was writing materials on the desk, without raising his head, he said, "Is it just Chen Zhou?"

Huang Yemei asked in surprise, "How do you know?"

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

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 the students in our mathematics department."

Huang Yemei was slightly taken aback, not understanding what Wu Xiping meant, she said: "Nothing happened to the freshmen in the Department of Mathematics recently. I have been to all the students' dormitories during the first two months of school, and they are all pretty good. "

Wu Xiping asked: "Then when you went to Chen Zhou's dormitory, didn't you notice any difference?"

Huang Yemei thought for a while and replied, "Well, Chen Zhou wasn't there when I went. According to other students, it seems that I went to the library to read."

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

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

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

Now that I think about it carefully, she found out that something was wrong, so she took away the books not long ago, and there are two books with handwriting?Did you read it, or did you draw it by hand?

Wu Xiping brought the test papers for this exam, found Chen Zhou's, and read them over.

There are 7 big questions, the answers are neatly written, the thinking is clear, and the answers are all correct.

Wu Xiping took out a red pen, stroked it a few times, and wrote down the number "101" in bright red.

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 and said: "This kid, it's expected."

Huang Yemei could hear a hint of appreciation from Wu Xiping's tone.

Although she has not been a counselor in the Department of Mathematics for a long time, she has also heard of Wu Xiping.

Wu Xiping's score test paper, the students complained again and again, either out of class or out of class.

Some students even choose to lose a few points because of this and choose to retake.

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

"By the way, if the undergraduates of our school apply for the project independently, do they have any requirements?" Wu Xiping usually takes the project in addition to being a substitute teacher. He knows about the school's regulations on this aspect, but he is not familiar with it.

Huang Yemei asked suspiciously: "Undergraduate student? Is it the Shen Jing you have been carrying around?"

Shen Jing was a student, but Huang Yemei knew about it. Since her sophomore year, she had been doing projects with Wu Xiping.

Now that Shen Jing is a junior, if he is good enough, he can indeed apply for a project independently, but according to the school's regulations, it is still difficult, very difficult.

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

Huang Yemei was slightly taken aback. Why is it Chen Zhou again? Even if he got full marks in the exam, he wouldn't be able to apply for a project, would he?Isn't this a freshman who has just entered school for two months?
(End of this chapter)