universal data

Chapter 356 I've Got It Done!

359 chapter

As soon as Dean Wei's smiling words came out, Cheng Nuo's expression couldn't help but change.

A thesis arguing for a logical error?
Allow yourself to find the mathematical language logic errors in it within half an hour?

Cheng Nuo frowned, thinking about the difficulty of the test that Dean Wei gave.

However, it is difficult for him to give an accurate conclusion without reading the entire paper.

Whether it can be completed, even if he is as confident as him, there is a big question mark!

But, at this moment, he doesn't have the option to "reject"!

Facing Dean Wei's smiling face, Cheng Nuo nodded heavily, "Okay, yes."

Dean Wei narrowed his eyes and pointed to a seat in the back row of the defense classroom, "You can answer the questions there first, and we will continue to interview other students who are defending."

Of course, it was impossible for the four teachers to sit here and wait for Cheng Nuo to finish answering for half an hour.

Just taking advantage of this time, you can finish interviewing one or two defense graduates.

Dean Wei was not worried 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 free manuscript, it was never published on any platform at all.

As for the logical error in the paper, it is even more impossible to find out through abnormal means.

Everything can only depend on Cheng Nuo himself.

This was also the ultimate test of Cheng Nuo's math level.

Even if Cheng Nuo failed to complete the answer in the end, Dean Wei would not refuse to give Cheng Nuo a graduation certificate, but Cheng Nuo's weight in his heart would definitely be greatly reduced.

Regarding the allocation of follow-up scientific research resources, it will also be readjusted.

Cheng Nuo took Dean Wei's thick thesis and came to a seat in the back row of the defense classroom.

In the drawer hole of the seat, there is a stack of draft paper and various stationery such as carbon pens.

It seems that Dean Wei has premeditated this!

Cheng Nuo smiled wryly, no matter whether he knew about it or not, he had no choice but to jump into it!

The thesis has a total of 34 pages, a few pages less than the one Cheng Nuo submitted.

The thesis title and thesis proof questions are exactly the same as Cheng Nuo's, both of which prove Bertrand's hypothesis.

The only difference is that the proof method mentioned by Cheng Nuo is a correct, reasonable and feasible proof scheme.

But Dean Wei's is a wrong proof scheme.

Hahaha!
If you think about it this way, it really feels much better!
Cheng Nuo's heart was swept away by the haze of being plotted by Dean Wei.

He moved his fingers, rubbed his face that was a little stiff because he had been smiling before, lowered his head, and began to browse Dean Wei's thesis.

Concentrating on it, he chewed up the contents of the thesis bit by bit.

He didn't even notice that the first four teachers communicated with the respondent graduates.

Although Dean Wei's thesis and Cheng Nuo's graduation thesis chose the same proof topic, the specific proof steps are quite different.

Both Cheng Nuo and Chershev, the great mathematician of the last century, used the method of lemma substitution and derivation when proving Bertrand's hypothesis.

But in this thesis of Dean Wei, he took a different approach and adopted a completely different way of proof.

Euler product formula introduction method!
Cheng Nuo named it this way for the time being.

In the thesis, Dean Wei introduced the concept of the Euler product formula from the very beginning of the proof process, and then deduced 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: Σn ns =Πp(1-ps)-1.

This is a rather unpopular mathematical formula, which is hardly used in current academic research on mathematics.

Unexpectedly, Dean Wei would come up with a whim and use it as another entry point to prove Bertrand's hypothesis, and he really deserves to be a big cow in the mathematics field of Huaguo.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 did not mean that Cheng Nuo had read the entire 34 pages of the document.

Just like the graduation thesis submitted by Cheng Nuo, it was really real, only five or six pages of content.

After reading it, Cheng Nuo understood Dean Wei's proof ideas.

First, he assumes that f(n) is a function satisfying f(n1)f(n2)=f(n1n2), and Σn|f(n)|<∞ (n1 and n2 are both natural numbers), then it can be deduced smoothly : Σnf(n)=Πp[1+f(p)+f(p2)+f(p3)+].

After deriving the above series of derivation theorems, the first step of the proof is completed.

Below, since Σn|f(n)|<∞, 1+f(p)+f(p2)+f(p3)+ absolutely converges.Consider the part of p < N in the continuous product (finite product)...Using the product property of f(n), it can be obtained: Πp<N[1+f(p)+f(p2)+f(p3)+]= Σ'f(n).

第三步，由于 1+f(p)+f(p2)+f(p3)+= 1+f(p)+f(p)2+f(p)3+=[1-f(p)]-1……

the fourth step,……

…………

In the last step, (2n)!/(n!n!)=Πp≤2n/3 ps(p).Decompose the multiplication into two parts: p ≤√2n and √2n < p ≤ 2n/3... Thus, the Bertrand hypothesis is proved to be true.

Step by step, logically.

The idea is strange, but it seems to be within 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 it through and check it again. He first excluded the simple logical derivation parts of the paper and ignored it.

If that 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 would be too embarrassing.

There are a total of five places in the paper where there are huge amounts of calculations and meticulous derivation steps.

Cheng Nuo checked one by one.

"First, the reasoning of the summation on the right side of the Euler product formula and the ordinary finite product, firstly, all f(n) terms containing factor 2 on the right side of the equation are eliminated, and then..."

"Second, the distribution of prime numbers and two-step precision,..."

…………

"The fourth place, the substitution of the nature of f(n), f(2)Σnf(n)= f(2)+f(4)+f(6)+"

Suddenly, Cheng Nuo's eyes froze when he saw this part of the content.

He stared at a line of formulas, looked left and right, and then a faint smile appeared on the corner of his mouth.

I found you!
Cheng Nuo picked up the carbon pen, wrote and drew on the draft paper for a while, and then heavily drew a horizontal line under the formula in the thesis.

横线上的公式：Πp[1-f(p)]Σnf(n)= f(1)= 1，(2n)!/(n!n!)=Πp≤√2n ps(p)，Σnf(n)=Πp[1-f(p)]-1
It's 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 several core formulas in the proof process of the entire paper. Therefore, errors in the formulas cause the entire paper to become a wasteful manuscript.

Cheng Nuo was in an extremely good mood at this moment.

Because not only did he find the logical error requested by Dean Wei, but he also calculated a reasonable correction plan in his mind!

Looking up, there was no one in the defense table in front of the four teachers.

Cheng Nuo picked up the paper and strode up to the podium.

Then, under the slightly astonished eyes of the four teachers, they smiled faintly, "Teacher, I've already done it!"

(End of this chapter)