The days of learning black magic in another world

This sentence seems to confirm the worry of the big man Freddy to some extent - Riemann really feels that they are not strong enough to be used as experimental materials for him, and he is not even willing to start with better-trained children. Instead, have you decided to backfire on them, the grown-ups?

But, but!

Freddy breathed a sigh of pride for no reason!

How can the children be allowed to bear the danger alone, their old arms and legs should stand in front of the danger for them.

If Riemann knew what he was thinking, he would probably only say: "...you think too much."

Riemann and Freddy returned to the fire group, and the children were still chatting together, and they didn't know what they were discussing, so Riemann turned to Freddy and said, "Then put... um, Gather people over 15, I'll give you a lesson first, Al and they're still discussing their ideas."

……

Riemann looked at the row after row of people sitting in front of him, released a [Summoning Light], and he looked at a piece of paper and a pen in their hands: "Uh, a piece of paper is probably not enough to take notes, Take a few more chapters."

When the others were ready, Riemann also squeezed out a slate, ready to start class.

"At your age... let's start with the real numbers."

"I know that your knowledge of numbers is closely related to magic, but I still decided to introduce numbers from normal logic."

"The simplest, easiest to be realized by human beings, and the number that is abstracted and summarized is a positive integer. We add a 0 to it, which is a natural number. Natural numbers are closed to addition and multiplication. The meaning of this sentence is, 1 1 equal to +2 is still a natural number, 1 equal to 2 times 2 is still a natural number, any two natural numbers added, multiplied, the result is still a natural number, then it is not closed to what?"

"Subtraction."

"If there are five wild fruits in front of me, and I eat three of them, if I abstract this process into a formula, it will be 5-3=2. This kind of subtraction is more intuitive, and it is commonly used in life, and it is the easiest to be abstracted. Yes, and the answer is still in the natural numbers."

"But if the formula is 3-5, we can't find a number from the natural numbers as its answer, but this formula is still meaningful. For example, I have three silver coins now, but I bought a book. If you want five silver coins, then I owe the bookstore owner two silver coins at this time."

"Thus we extended the range of numbers to integers, that is, we added the concept of negative numbers."

"Right now, integers are closed for addition, multiplication, and subtraction, but it's still not good enough."

"We will encounter such a situation, now eight people go out to collect wild fruits, and we have picked sixteen wild fruits, then we will naturally divide 16 equally among 8 people, and get the formula 16/8=2, that is Division, integers are not closed to division, such as 2/3, the result is not an integer, so we expand the range of numbers to rational numbers."

"I know you're more used to calling this a fraction, but I prefer to call it a rational number, so make a note of that word and you'll know what it stands for later."

"Here we define a rational number. We define a rational number as p/q, where pq is a relatively prime integer, q is a positive integer, and p is an integer."

"The range of rational numbers is large enough for most calculations, but it doesn't cover all numbers."

"For example, the classic root number 2, let's prove that the root number 2 is not a rational number, that is to say, the root number [-] cannot be expressed as a fraction."

"We employ a method of proof by contradiction."

"Assuming that the square root 2 can be expressed as a rational number of the form p/q, where pq is a coprime integer, then we can obtain an equation p?=2q?."

"Let me emphasize again, we assume that p and q are both integers, so in this case, p must not be an odd number, because the square of an odd number cannot have a factor of 2, right?"

"So we deduce that p is an even number, and even numbers can be expressed as 2k, where k is an integer."

"So we got another equation, 2k?=q?, similarly, q is an even number."

"That is to say, from the premise that the square root 2 is a rational number, we can deduce such a result that p and q have a common factor 2, which violates the original assumption that pq is relatively prime, and thus the premise is that Incorrect."

"Based on similar ideas, we can also prove that the root number 3 and the root number 12 are irrational numbers."

"And here, I want to introduce the concept of infinity for the first time. Now I draw a line segment. The starting point of this line segment is 0 and the end point is 1. That is, it is a finite line segment with a length of 1."

“那么请思考这样一个问题，如果我要从0走到1，那么我得先走到0和1的中点1/2，如果我要从0走到1/2，那么我就需要先走到0和1/2的中点1/4，而这个过程是可以无限继续下去的，你们看到问题所在了吗？”

"The second example is still this line segment. I erect it, and then I draw a slightly inclined line segment next to it, which is a bit like the height and hypotenuse of a right triangle, right?"

"The lengths of these two line segments obviously do not want to wait, but we can match the above points one by one and connect the lines horizontally. Yes, assuming that the line segment is composed of countable points one by one, then we will get An absurd conclusion, that the two line segments are equal."

"But we know that they are not equal, so I think you should have come to the conclusion that even a finite line segment is covered with infinite numbers, right?"

"Very well, that's all you need to know about real numbers for now."

"Let's talk about assembly next."

……

Missy slipped out of Al and the others halfway and came to Mr. Riemann's "classroom".

Mr. Riemann placed the Summoning Light above the slate, a ball of light bright enough for her to see her mother's notes on paper.

"Mom, show me."

"Oh! Missy! When did you come here?"

"just."

Missy's mother took out a few sheets of paper she had placed underneath and handed them to Missy, while she continued to listen to the class and take notes.

Missy quickly glanced at the few pieces of paper, then raised his head to look at Mr. Riemann who was talking under the white light.

"...another property of collections to be aware of is that repetition of elements is meaningless."

"Let's take an example to understand. Everyone should remember that the definition of a set is a collection of objects with certain properties, so I'm going to say something here-who wants to go hunting with me? Is the person who signed up a set? "

"In this case, suppose I accidentally wrote Mr. Freddy's name down twice, and I now have 18 names on the paper, and there are two Freddy's, it doesn't mean that there will be two Freddy came to hunt with me, didn't he? There were still only 17 people who actually went hunting with me, and only one Freddy, which is the pointlessness of repetition."

Missy thinks that Mr. Riemann is a magical person. He always likes to give various examples. She actually thinks this is a waste of time, but others seem to think it is easier to understand. Alas, then she can only accommodate Others who are not smart enough.

"...Another thing to watch out for with the assembly is, uh, wait a minute."

Missy watched as Mr. Riemann took out a piece of paper from nowhere, his pretty eyebrows frowned slightly, and then he turned his head and said to everyone: "Sorry, I'm here first for today's class, although there is nothing to understand However, I hope that everyone can spend some time remembering these basic concepts, because we will use them frequently in the future. If there are any forgotten ones, you can exchange notes with each other and perform a check to fill in the gaps. I have some things to do, see you tomorrow. "

Missy couldn't help but let out an annoyed "Oh—" She just arrived!How come it's over before it starts!

But she didn't feel upset for long, because her mother tugged at the corner of her clothes: "Missy, help me see the part that proves the square root of 2..."

"Okay, Mom."

……

The reason for Riemann to stop his lecture halfway is naturally the news of the abyss.

Before he left Bishop Pound and the Son of God, he gave them a temporary small teleportation formation—the small formation means that it is really very small, only enough to send a note.

It was a super small map with six x's on it, which meant that there were changes in the abyss in these six places.

Riemann raised his eyebrows. No wonder Bishop Pound's attitude was so uncooperative at the time, but he still came to him now. There were six abnormalities at one time, and the Holy See was probably in a hurry.

Riemann checked his equipment and teleported away immediately.

"Twisting vines."

"Summon · Fire."

"Summon Wind."

Riemann's routine of spawning monsters is so simple.

This set is just clean.

In fact, he has recently been thinking about whether he can simplify the skills needed to spawn monsters to a single one, although it seems he is a bit lazy... and it took him a long time to find the place after teleporting from thousands of miles, but in the end, the battle ended with only one skill, Always seemed a little... top-heavy, but he wanted to do it anyway.

In fact, the advanced magic of [Vine Entangling] in his hand is very suitable.

The higher-level magic of the second-level magic [Vine Entangling] is the fourth-level magic [Vine Strangling]. In addition to controlling and dispensable damage, it also adds a large amount of damage and a small amount of blood-sucking effect. The only problem is that it is a fourth-level magic. magic.

Riemann glanced at his experience bar. Today, he killed more than [-] abyss monsters, and the experience bar only moved by a quarter. This is really a sad story.