Into Unscientific

  Chapter 25 Han · Mathematics Wizard · Li (seek to follow up!!!)

  In the room, Xu Yun was talking eloquently:

"Mr. Newton, Sir Han Li calculated that when the exponent in the binomial theorem is a fraction, you can use e^x=1+x+x^2/2!+x^3/3!+…+x^n/ n!+… to calculate."

   As he spoke, Xu Yun picked up a pen and wrote a line on the paper:

  When n=0, e^x＞1.

   "Mr. Newton, here starts from x^0. It is more convenient to use 0 as the starting point for discussion. Do you understand?"

   Maverick nodded, indicating that he understood.

   Then Xu Yun continued to write:

  Assume that the conclusion is true when n=k, that is, e^x＞1+x/1!+x^2/2!+x^3/3!+…+x^k/k!（x＞0）

  Then e^x-[1+x/1!+x^2/2!+x^3/3!+…+x^k/k!]＞0

Then when n=k+1, let the function f(k+1)=e^x-[1+x/1!+x^2/2!+x^3/3!+…+x^(k +1)/(k+1)]! (x>0)

   Then Xu Yun drew a circle on f(k+1) and asked:

   "Mr. Newton, do you know anything about derivatives?"

   Maverick continued to nod, and said two words concisely:

"learn."

   Friends who have studied mathematics should know it.

  Derivative and integral are the most important components of calculus, and derivative is the basis of differential and integral.

  It is now the end of 1665, and Mavericks' understanding of derivatives has actually reached a relatively profound level.

  In terms of derivation, the intervention point of Mavericks is the instantaneous velocity.

  Speed=distance/time, this is a formula that elementary school students know, but what about the instantaneous speed?

  For example, if you know the distance s=t^2, then when t=2, what is the instantaneous speed v?

  The thinking of a mathematician is to transform unlearned problems into learned problems.

  So Newton thought of a very clever way:

  Take a "very short" time period △t, first calculate the average speed during the time period from t=2 to t=2+△t.

  v=s/t=(4△t+△t^2)/△t=4+△t.

  When △t is getting smaller and smaller, 2+△t is getting closer to 2, and the time period is getting narrower and narrower.

  △t is getting closer to 0, then the average speed is getting closer to the instantaneous speed.

  If △t is as small as 0, the average speed 4+△t becomes the instantaneous speed 4.

Of course.

  Later, Berkeley discovered some logical problems of this method, that is, whether △t is 0 or not.

  If it is 0, how can △t be used as the denominator when calculating the speed? Few people cough, elementary school students also know that 0 cannot be used as a divisor.

  Until it is not 0, 4+△t will never become 4, and the average speed will never become the instantaneous speed.

  According to the concept of modern calculus, Berkeley is questioning whether lim△t→0 is equivalent to △t=0.

  The essence of this question is actually a kind of torture for the nascent calculus. Is it really appropriate to use the moving and fuzzy words like "infinite subdivision" to define precise mathematics?

  The series of discussions triggered by Berkeley is the famous second crisis of mathematics.

There are even some pessimistic parties claiming that the building of mathematics and science is about to collapse, and our world is all false—then these goods really jumped off the building, and there are still their portraits in Austria. Like the seven dwarfs, I don't know whether it is used to be admired or to whip corpses.

   This matter did not have a complete explanation and conclusion until the appearance of Cauchy and Weierstrass, and it really defined the tree that many students in later generations hung.

   But that was a later thing. In Mavericks' age, the practicality of freshman mathematics was given top priority, so strictness was relatively ignored.

  Many people in this era use mathematical tools to do research, and use the results to improve and optimize the tools.

   Occasionally, there will be some unlucky people who think about it and suddenly find that their research in this life is actually wrong.

all in all.

  At this point in time, Mavericks is quite familiar with derivation, but has not yet summarized a systematic theory.

  Xu Yun saw this and wrote:

Deriving f(k+1), we can get f(k+1)'=e^x-1+x/1!+x^2/2!+x^3/3!+…+x^k /k!

   From the assumption that f(k+1)'＞0

   Then when x=0.

  f(k+1)=e^0-1-0/1!-0/2!-0/k+1!=1-1=0

  So when x>0.

  Because the derivative is greater than 0, f(x)>f(0)=0

So when n=k+1 f(k+1)=e^x-[1+x/1!+x^2/2!+x^3/3!+…+x^(k+1) /(k+1)]! (x>0) established!

  Finally, Xu Yun wrote:

  In summary, for any n:

  e^x＞1+x/1!+x^2/2!+x^3/3!+…+x^n/n!（x＞0）

  After finishing the discussion, Xu Yun put down the pen and looked at Mavericks.

  I saw this moment.

  The patriarch of later generations of physics is staring at the draft paper in front of him with his bull's eyes wide open.

   True.

  With the current research progress of Mavericks, it is not very easy to understand the true inner meaning of tangent and area.

  But anyone who knows mathematics knows that the generalized binomial theorem is actually a special case of the Taylor series of complex variable functions.

   This series is compatible with the binomial theorem, and the coefficient signs are also compatible with composite signs.

  So the binomial theorem can be extended from natural number powers to complex number powers, and the combination definition can also be extended from natural numbers to complex numbers.

   It's just that Xu Yun kept a hand here and didn't tell Maverick that when n is negative, it is an infinite series.

  Because according to the normal historical line, the infinitesimal amount was created by Mavericks, so it is better to leave the derivation process to him.

   After a few minutes like this, Mavericks just came back to his senses.

  I saw him directly ignoring Xu Yun who was beside him, and rushed back to his seat, and quickly began to calculate.

  Looking at Mavericks who was devoting himself to calculations, Xu Yun was not angry either. After all, this patriarch had such a temper, and he might be relatively better in front of William Escue.

  Shushasha—

soon.

  The sound of the tip of the pen touching the manuscript paper sounded, and formulas were quickly listed.

   Seeing this, Xu Yun thought for a moment, then turned and left the room.

   Randomly found a place in the corner, looked up at Yunjuan Yunshu.

   Just like that, two hours passed by.

   Just as Xu Yun was thinking about what to do next, the door of the wooden house was suddenly pushed open, and Maverick rushed out from inside with an excited expression on his face.

   His eyes were bloodshot, and he waved the manuscript in his hand vigorously to Xu Yun:

   "Fat fish, negative numbers, I rolled out negative numbers! Everything is figured out!

  The binomial index does not care whether it is positive or negative, whether it is an integer or a fraction, the combination number is true for all conditions!

   Yang Hui triangle, yes, the next step is to study Yang Hui triangle! "

   I don't know if it was because of being too excited, Maverick didn't even notice that his wig was shaken to the ground.

  Looking at the red-faced calf, Xu Yun couldn't help feeling a sense of excitement about changing history.

  Follow the normal trajectory.

   Mavericks will not be able to overcome a series of doubts and difficulties until they receive a letter from John Tisripodi in January next year.

  In the letter of John Seri Porti, it is Pascal's public triangular figure that is mentioned.

   That is to say

   This node in the history of space-time mathematics has been changed for the first time!

  With the preliminary results of the binomial development, Mavericks will surely build a preliminary flow number model with the assistance of Yang Hui's triangle in a short time.

   From this.

  The name Yang Hui Triangle will also be engraved on the base of the Mathematics Throne, where it should have been!

  Even if the world changes in the next few hundred years and the vicissitudes of life, no one can shake it!

  The light of Chinese sages will never be dusted in this timeline!

  Thinking of this, Xu Yun couldn't help but take a deep breath, and walked forward quickly:

   "Congratulations, Mr. Newton."

  Looking at Xu Yun with an oriental face in front of him, Maverick also felt a wave of emotion on his face.

  The Sir Han Li, whom he had never met, could see the light of day for himself with just a few essays left behind, and he could open a door for himself with the help of Fat Yu, a disciple who didn't know how many generations apart.

  Then how high can Sir Han Li's knowledge reach?

   A genius who can come up with this kind of expansion is not an exaggeration to be called a mathematical genius, right?

  At first, I thought that Mr. Descartes was invincible, but I didn't expect that there would be someone more brave than him!

  It seems that my road of mathematics and science still has a long way to go.

Note:

  Why the out-of-circle index is negative.

   I heard that there are no video rewards now, because some studios organized groups to collect wool

  (end of this chapter)