"Learn, gain knowledge." Since Ye Fei discovered the power of the system, he naturally attached importance to the application of the system.

"Read the paper for one hour, and the task progress is 2%."

"Reading books, reading papers, and listening to lectures are all learning."

"Learning is a long process, and it is impossible to quickly improve the knowledge reserve in a short time, which can only be settled with the encounter."

"And now the priority is to do the task."

"I just looked at the paper to find mistakes, and the progress of the task was accelerated."

"This is when inspiration should be more forthcoming."

"But if you go to arxiv to find paper mistakes, you might as well go to Stack Exchange and discuss math with others."

"This should speed up the mission."

With that, he opened the Stack Exchange website.

The Stack Exchange website is a global open website where many scholars in various fields ask questions and answer questions.

Ye Fei opened the math section and saw that there were many questions on it, he browsed at random, and when he saw an interesting question, he would answer it, and when he saw an interesting answer, he would also interact with it.

He found that by doing so, the progress of the task increased very quickly.

It's just an hour, and his quest progress is increased by 5%.

"Huh?" Ye Fei suddenly clicked on a post: "Cantor's two mistakes in set theory? ”

"Cantor's mistake?" Ye Fei laughed: "This person is really bold, isn't he afraid of being sprayed when he says big things?" ”

Cantor is Georg Cantor, the founder of set theory and the man who proposed the continuum hypothesis.

Set theory has been around for nearly a hundred years, and that's when someone jumped out and said that Cantor's set theory was wrong.

It's as if someone said that Einstein's theory of relativity was wrong.

If he is a celebrity who is close to or equal to Cantor in mathematics, others will think about it.

If the difference in ability is too great, if you say it, anyone who sees it will want to spray him.

Ye Feixin said: "Let's take a look first." ”

With that, he looked at the text.

[Analyzed Cantor's uncountable proof of the set of real numbers and Cantor's theorem......]

"Huh?" Ye Fei frowned suddenly: "This seems to be really wrong!" ”

"No, it should be said that it is not a mistake in the Cantor set, but that he has a very clever problem, which leads to the continuum hypothesis."

"It is said here that Cantor proves that the set of real numbers is uncountable, using the interval nest method and the diagonal method."

"In these two proofs, the method of refutation is used."

"And the uncountable set of real numbers is the continuum hypothesis."

"The continuum hypothesis did not prove successful, which is naturally Cantor's mistake."

"Hey......" Ye Fei laughed: "This person is really a chicken thief, is this an inappropriate title party!" ”

"Hmm......" Ye Fei pondered for a moment, and suddenly his eyes lit up: "It can be solved like this!" ”

"Although the continuum hypothesis cannot be fully proven, this idea may solve some minor problems."

After speaking, Ye Fei left a message below.

[Proof: First proof, because for any x∈s, let ƒ(x)={x}, and x1≠x2 ......]

North Liguo, MIT Doctoral Student Dormitory!

A yellow-skinned young man was staring boredly at the computer screen with his chin propped up, waiting for someone to reply to his message.

The young man's name is Gao Fei, Xia Guoren, Ph.D. from MIT.

His main research is not set theory, but recently there has been research on set theory.

To study set theory, it is natural to study the continuum hypothesis.

So, two hours ago, he posted to Stack Exchange about the collection of real numbers.

In order to attract traffic, he deliberately wrote that Cantor was wrong in set theory, which he did often, tried and tested, and attracted a large wave of people each time.

Occasionally, he can attract a message from a big man, which can make his research on mathematics suddenly brighter.

Slender fingers slid the mouse scroll and browsed the web.

"Huh?" He stopped abruptly, straightened up, and fixed his eyes.

"Using Russell's paradox to prove that a set of real numbers is uncountable?"

His eyes twinkled, and he took the pen and paper on the side to calculate.

After a while, he said excitedly: "That's it, but what he said is not perfect, and it should be so." ”

He quickly left a message under Ye Fei's message.

[Thank you for your reply, which inspired me, but I think I should add the following.]

If x∈s is true, according to the requirements for the elements in s in Eq. (3......

……

If x∉s, get x∉φ(x)...... from s=φ(x)]

He had received a reply less than ten minutes after he sent it.

Goofy was surprised: "So fast? ”

"Looks like he's just like me, staying in front of the computer, looking forward to the answer!"

[Thank you for the addition, but I would also like to add to the following.]

Whether X belongs to S or not, it leads to contradictions......]

After reading it, Gao Fei smiled and said, "This idea is very good. ”

After speaking, he took the pen and paper again, and replied to the other party after thinking for a while.

Ye Fei also thought for a moment after reading it.

The two of them replied back and forth, they didn't know who they were, but at this time, they seemed to have found a spiritual fit.

Goofy was excited, he hadn't met anyone who inspired him mathematically in a long time.

"I don't know which big guy it is?" Gao Fei said in his heart, he described in his mind a middle-aged man in his thirties and forties, with a vague appearance, and he didn't know whether it was a man or a woman.

He is a genius, and it is difficult to meet a genius like him at MIT, the world's number one university in science and engineering.

Therefore, almost no one of his peers in the past could give him mathematical inspiration, only those who had studied mathematics for many years would give him inspiration when discussing mathematics with him.

Therefore, Ye Fei was a middle-aged man in his mind at this time.

Ye Fei was also very excited, in this year of graduate school, he may be the only one among the tutor's students who has been admitted to graduate school, so the tutor is the strictest of all the students.

This year, he read a lot of literature.

Therefore, at this time, his knowledge reserves, with the help of the system, were integrated and burst into countless inspirations.

After a long time, the two ended their conversation, and as they watched as they wrote a large dialogue, Goofy copied down all the math content.

He left a message for Ye Fei backstage and said, "Let's pay attention to each other!" ”

It is difficult to meet someone who can communicate with him academically, and when you meet such a person, you must get to know him, and if there are mathematical problems in the future, you can also discuss them.

Ye Fei: "OK! ”

For the sake of increasing his task by 50%, Ye Fei agreed to his proposal.

After that, the two looked at each other.