Although Su Mufeng had already expected the fierce reaction of Mo Zhai and the others, he was a little underestimated about the fierce specific Cheng Dù.

But after all, the wood is already in the boat, and Su Mufeng can only continue to speak.

I hope to leave a little fragment of the worldview of this group of people...... He complained silently in his heart.

"Mo Sheng, in the field of mathematics and physics in the countries of Middle-earth, can you briefly elaborate on the concept of continuity of 'number'?"

After thinking for a while, Su Mufeng decided to adopt a step-by-step approach to slowly inculcate that concept.

-- The concept that triggered the first mathematical crisis that lasted for 2,000 years.

Mo Zhai pondered for a moment and said, "In the process of sorting out the works of mathematical masters in history, Zhai briefly analyzed the continuity characteristics of numbers. In Zhai's view, the number of all things can be divided into two kinds, one is the whole and the other is the approximation, and the approximate number is the ratio of the integer number. ”

"The process of change of numbers is consistent and continuous, and integers, as the most basic quantity, are interspersed with divisors in the changes of integers and integers, and the whole reductions are interspersed to form the continuity of numbers."

"However, now it seems that Zhai's idea is probably wrong...... Mo Zhai smiled bitterly: "Moreover, it is ridiculously wrong!" ”

A few drops of cold sweat slipped down Su Mufeng's forehead.

Mo Zhai is worthy of being a generation of demi-saints and the leading natural scientist of the Spring and Autumn Period and the Warring States Period.

In what he just said, there was already a rudimentary form of the concept of "arithmetic continuum"! The construction of the rational number system has also reached the realm of basic perfection!

However, as Mo Zhai said, there is one of the biggest loopholes in his theory.

"I'm sorry, Mo Sheng, you were wrong."

Su Mufeng sighed and said slowly: "Rational numbers, that is, the integers and divisors you are talking about, do not completely summarize the range of numbers. ”

Mo Zhai sighed lightly: "The hook is one, the strand is one, the number represented by that string is what Zhai missed, right?" ”

Su Mufeng nodded and said, "The string length is the root number two-you can call it, irrational number." ”

Although it was already expected, when he heard Su Mufeng admit the existence of "irrational numbers", Mo Zhai's complexion still changed, and even a little pale.

He sighed, got up again, and personally brought a cup of tea to Su Mufeng.

"May Mr. Su teach."

Su Mufeng didn't have much surprise at Mo Zhai's expression, but just took the teacup with a wry smile and drank it all.

Irrational number.

The first devil in the history of mathematics to lurk in the details.

Irrational numbers, which have unfairness, completely negate the completeness and arithmetic continuum of rational numbers at the moment of their birth.

On Earth, in ancient Greece in 500 BC, Hippasus, a disciple of the Pythagorean school, discovered the existence of irrational numbers for the first time.

Its origin is precisely the problem of "Pythagorean uniformity" caused by the Pythagorean theorem.

The existence of the second root number completely rejects the core theory of the Pythagorean school that "everything is numbered" and "all numbers are reasonable".

The last choice of the panicked Pythagoreans was to throw Hypassos into the water and kill him, the first scientist in history to be murdered for his academic achievements ahead of his time.

The challenge and crisis to the rational number system caused by the unfairness represented by irrational numbers did not end with the death of Hippasus.

It was not until 1872, two thousand years later, that the German mathematician Dedekind, starting from the requirement of continuity, defined irrational numbers with the "division" of rational numbers, and based the theory of real numbers on a strict scientific basis, which ended the era when irrational numbers were considered "irrational".

It also ended the first major crisis in the history of mathematics that lasted for more than 2,000 years.

And in the undeveloped continent of Middle-earth, where the field of mathematics and physics is still undeveloped, how terrible will the impact of the concept of "irrational numbers" be?

Su Mufeng only needed to look at Mo Sheng's face to be clear.

As a demi-saint, Mo Zhai has gone through hundreds of years of vicissitudes of life, and he can barely maintain his peace at this moment. His disciples were completely different, their faces were as pale as paper, and their expressions were horrified.

If mathematics and physics were also included in the list of the Holy Dao, I am afraid that these people would have already collapsed because of the self-collapse of the Holy Dao and their talents.

In order not to cause irreparable damage to Mo Sheng's worldview as much as possible, Su Mufeng began to elaborate in a circular and gradual manner.

"To analyze the definition of irrational numbers, we must first start with its unfairness......

So, in the following time, only Su Mufeng's voice was left in the quiet room.

Everyone else, including Mo Zhai, was sitting upright, intently listening to Su Mufeng's lecture.

Mo Yunfei had already put away his original hostility, and when he listened to the lecture respectfully, he was still remorseful and ashamed of the ignorant provocation just now.

Even Mo Yu, who was not convinced at first, completely put away his contempt.

Listening to this, there was a hint of reverence in the little girl's eyes.

Among the crowd, only Mo Zhai could still maintain a relatively peaceful state of mind, asking a few small questions from time to time. Of course, there are also occasional exclamations.

Finally, after a period of time, Su Mufeng had roughly elaborated the concept of irrational numbers.

But everyone was still pondering, and did not come back to their senses.

After a long time, Mo Zhai finally woke up from his contemplation and sighed: "The sea of ups and downs and fog has been hundreds of years, and now the big dream has just woken up. ”

Su Mufeng said: "The hundreds of years of Mosheng's dream are the foundation for future generations to move forward in mathematics and physics, so there is no need to be arrogant. ”

Mo Zhai smiled and said: "But Mr. Su's attainments in mathematics and physics have reached such a state, but he has never read the "Book of Ink"! ”

Su Mufeng was dumbfounded for a while, after all, he really hadn't read it, and most of it was almost lost in the Qin Dynasty, right?

Mo Zhai smiled: "Mr. Su doesn't need to be modest anymore, one day Mr. Su's works will spread all over the world, and there will be nothing to do with Zhai's "Book of Ink". ”

Su Mufeng waved his hand again and again: "I'm sorry, I'm sorry, you're thinking too much, I don't plan to publish any books." ”

This kind of great achievement, let's leave it to Xiao Han Fei to complete, he only needs to be responsible for drinking tea and dictating his memoirs.

Mo Zhai thought that Su Mufeng was joking, and quipped: "Mr. Su didn't write a book of "Suzi", and the Great Dao was lost, which is a pity for the entire Eastern Zhou Dynasty." ”

Mo Zhai's words reminded Su Mufeng, and he thought for a moment and said: "The Pythagorean theorem and the concept of irrational numbers I just mentioned, how about bothering Mo Sheng to write it into the Book of Ink?" ”

There was a moment of silence in the room.

Even with Mo Zhai's city government, he couldn't help but be shocked at this time: "Mr. Su must not!" ”

Mo Yu on the side couldn't help but say: "If Mr. Su does this, the whole world will laugh at the Mo family." ”

Mo Yunfei nodded on the side.

Su Mufeng's reaction to Mo Zhai was not surprising, but Mo Yu and Mo Yunfei's rebuttal made him a little stunned.

Wasn't that girl still in opposition just now? Why did you turn your head and call Mr. Shang?

And that big brother, the villain has a firm stance, okay?

Glancing at the two of them in confusion, Su Mufeng explained to Mo Zhai: "Among the countries of Central-earth, Mo Sheng is a master of mathematics and physics, and only the theory written into the "Book of Ink" can be widely recognized by the world. ”

This is the role of authority, Su Mufeng doesn't want to provoke a group of Pythagorean apologists and throw him into the sea.

Moreover, Su Mufeng and Mo Zhai discussed natural science, not just to "cheat skill books".

His true purpose, which may sound a little sublime and paranoid, is indeed valid.

That is to leave a seed for the Middle-earth continent.

The Central Continent has almost lost the soil for the development of natural sciences, and will inevitably embark on a completely different path of civilization from the earth.

However, as the saying goes, the pinnacle of natural science and literature is nothing more than a highly developed economic foundation and a highly civilized superstructure.

In the process of the development of the cultural and Taoist civilization in the Middle Continent, perhaps the natural sciences can also play a role, just as the Mohist mechanism is to other countries.

In addition, there is no doubt that ten years from now, Han Fei will surely embark on the road of conquest by other countries.

During this time, with the help of the Mo family, Su Mufeng may be able to leave some invisible wealth for Han Fei.

Mathematics is just the beginning.

……

……

Of course, it is also very important to find two skill books for Mo Sheng......