Chapter 359: I have done it!

Chapter 359
As soon as Dean Wei said with a smile, Cheng Nuo's expression could not help but change.
A paper demonstrating logical errors?
Let yourself find the logic error in mathematics language within half an hour?
Cheng Nuo frowned and thought about the difficulty of the test that Dean Wei gave.
However, it is difficult for him to give an accurate conclusion before reading the entire paper.
Whether it can be done, even if you are as confident as him, you have to put a big question mark!
However, at this moment, he did not have the option to "reject"!
Facing Dean Wei's smiling face, Cheng Nuo nodded his head, "Okay, yes."
Dean Wei squinted his eyes and pointed to a seat in the back row of the defense classroom, "You can answer the questions there first. We will continue to interview other students who are responding."
In half an hour, of course the four teachers could not sit here and wait for Cheng Nuo to finish answering.
Just take advantage of this time to interview one or two respondent graduates.
Dean Wei did not worry that Cheng Nuo would use his mobile phone to search for information on the Internet.
This paper was originally written by him, and because it was a costly manuscript, it has not been published on any platform at all.
As for the logical error in the paper, it is even more impossible to know it through abnormal means.
Everything depends on Cheng Nuo himself.
This can be regarded as the ultimate test of Cheng Nuo's mathematics level.
Although it was said that even if Cheng Nuo did not successfully complete the answer in the end, Dean Wei would not refuse to issue Cheng Nuo's diploma, but Cheng Nuo's weight in his heart would definitely be greatly reduced.
Regarding the allocation of subsequent scientific research resources, it will also be readjusted.
Cheng Nuo took Dean Wei's thick paper and came to a seat in the back row of the defense classroom.
In the drawer hole of the seat, there are stacks of scratch paper and various stationery such as carbon pens.
It seems that Dean Wei had planned for a long time!
Cheng Nuo smiled bitterly. Regardless of whether he knew it before, he had no choice but to jump into it!
The paper has 34 pages, which is a few pages less than the paper submitted by Cheng Nuo.
The title of the thesis and the proof of the thesis are exactly the same as Cheng Nuo, both of which prove the Bertrand hypothesis.
The only difference is that the proof method described by Cheng Nuo is a correct, reasonable and feasible proof scheme.
And Dean Wei's is a wrong proof scheme.
Hahaha!
If you think about it this way, it really feels much better!
The haze in Cheng Nuo's heart was swept away by Dean Wei's calculations.
He moved his fingers, rubbed the stiff face that he had been smiling before, lowered his head, and began to browse Dean Wei's paper.
Attentively, he chewed up the content of the paper little by little.
He didn't even notice the first four teachers communicating with the respondent graduate.
Although Dean Wei’s thesis and Cheng Nuo’s graduation thesis chose the same proof topics, the specific proof steps are very different.
Cheng Nuo and the great mathematician Chershev of the last century used the method of lemma substitution when proving Bertrand's hypothesis.
But in this thesis of Dean Wei, he took a different approach and adopted a completely different approach to proof.
Euler product formula introduction method!
Cheng Nuo is named after this for the time being.
In the thesis, Dean Wei introduced the concept of Euler product formula from the beginning of the proof process, and then proceeded to derive the proposition through the Euler product formula and the mathematical logic relationship assumed by Bertrand.
What is the Euler product formula?
This is one of the starting points for the distribution of complex numbers proposed by the mathematician Germain. The specific content is: For any complex number s, if Re(s)>1, then: Σnn-s=Πp(1-p-s)-1.
This is a rather unpopular mathematical formula, which is almost hard to use in current mathematical academic research.
Unexpectedly, Dean Wei would have a whim and use it as another entry point to prove Bertrand's hypothesis. It really deserves to be a big bull in Chinese mathematics. However, the result does not seem to be perfect.
It took more than ten minutes for Cheng Nuo to read the entire paper.
Of course, this does not mean that Cheng Nuo read the complete 34 pages of the document.
Like the graduation thesis submitted by Cheng Nuo, it is really true, only the five or six pages of content.
After reading it, Cheng Nuo understood Dean Wei's idea of ​​proof.
First, he set f(n) as a function satisfying f(n1)f(n2)=f(n1n2) and Σnf(n)∞ (n1 and n2 are all natural numbers), then it can be derived smoothly: Σnf(n )=Πp[1+f(p)+f(p2)+f(p3)+].
After getting the above series of derivation theorems, the first step of the proof is completed.
Next, since Σnf(n)∞, 1+f(p)+f(p2)+f(p3)+ absolutely converges. Consider the part of pN in the continuous product (finite product).........Using the product property of f(n), we can get: ΠpN[1+f(p)+f(p2)+f(p3)+]=Σ\'f (n).
The third step, since 1+f(p)+f(p2)+f(p3)+=1+f(p)+f(p)2+f(p)3+=[1-f(p) ]-1……
the fourth step,……
…………
The last step is by (2n)!/(n!n!)=Πp≤2n/3ps(p). The continuous multiplication is decomposed into two parts: p≤√2n and √2np≤2n/3... Thus, it is proved that Bertrand hypothesis is valid.
Step by step, the logic is strict.
The idea is simple, but it seems to be in common sense.
After reading it the first time, Cheng Nuo did not find any flaws in the paper.
Cheng Nuo frowned slightly.
Sure enough, things are not that simple.
Cheng Nuo didn't have time to read through it again. He first eliminated the simple part of the logical derivation in the paper and ignored it.
If the logical error really appeared in that low-level logical derivation step, it would be impossible for Dean Wei to use it as the topic of Cheng Nuo's thesis defense.
Because that's too shameful.
There are five places in the thesis where there is a huge amount of calculation and careful derivation steps.
Cheng Nuo investigated one by one.
"The first place is the reasoning of summation and ordinary finite product at the right end of the Euler product formula. First, eliminate all f(n) terms containing factor 2 at the right end of the equation, and then..."
"The second place, the distribution of prime numbers and two-step precision,..."
…………
"The fourth place, substituting the properties of f(n), f(2)Σnf(n)=f(2)+f(4)+f(6)+"
Suddenly, when Cheng Nuo saw this part of the content, his eyes condensed suddenly.
He stared at a line of formulas, looked left and right, then a faint smile appeared on the corner of his mouth.
I found you!
Cheng Nuo picked up the carbon pen, and after writing and drawing on the draft paper for a while, he then heavily drew a horizontal line under the formula in the paper.
The formula on the horizontal line ~EbookFREE.me~ is here, that's right.
There is a habitual error in the logical relationship between the third formula and the first two formulas.
These three formulas can be regarded as one of the core formulas in the proof process of the whole paper. Therefore, the errors of the formulas cause the whole paper to become a costly manuscript.
Cheng Nuo was in an extremely good mood at this time.
Because he not only found the logical error that Dean Wei requested, but also calculated a reasonable corrective plan in his mind!
Looking up, there was no one on the bench in front of the four teachers.
Cheng Nuo picked up the paper and swaggered onto the stage.
Then, in the slightly surprised eyes of the four teachers, they smiled faintly, "Teacher, I have done it!"