It just so happened that I once got sunburned. I was red as a tomato. My body was burning, I couldn’t move. I was very thirsty. Symptoms of the burn appeared at night, and I was in the south, where the electricity was cut off at night. There was nothing to do, but I couldn’t sleep because of the burns. I had to think to keep myself busy. I thought about all sorts of chipukha. First about ponies, then about Pallas’s cats, then about why the sky is blue and not grey-brown, then again about Pallas’s cats then… And so I thought and thought and came up with the idea of ​​dividing by zero. At first I couldn’t do anything, but then I started thinking like a kindergartener. I imagined apples and began to multiply them, then divide them in order to understand the meaning of these actions. Then I began to divide the apple by zero and an epiphany descended! I solved this mystery! Realized the mathematical symbolism of this action. I got out of bed like crazy, found a pencil (it was in the dark), then quickly drew the formulas for this division on napkins… And it started spinning..

This was 3 years ago, I was still a wild, uncultivated Pallas’s cat, who smelled strongly of schoolboy. And as part of my obsession with zero, I created a video lesson, it’s hard to watch, the diction is terrible (largely due to the player through which I recorded the sound), but I tried to convey the idea in it… It turned out badly. But I still want to show:

Buzz 🙂 Don’t take the video seriously, try to understand the essence 🙂 If that doesn’t work, then I suggest reading a thought experiment that I came up with half a year ago to better explain the problem of division by zero:

Zero is a very controversial number. It has been known since school years that one cannot divide by zero, otherwise the operation of the mathematical apparatus is disrupted. Since ancient times, the sophists, dividing by zero, provide evidence that 2+2=5, 3=7 and the like.
Division by zero causes uncertainty, so mathematicians decided to prohibit division by zero.
In limit theory there is division by zero, but we must remember that this division has nothing to do with algebra, it has its own meaning. And that zero is actually not zero, but an infinitesimal value. But many do not delve into the details and then claim that when divided by zero, infinity arises. In fact, this is not true, since zero and infinitesimal are completely different things.
It is known that prohibitions exist only to be broken. Therefore, now I will try to show the method of dividing by zero. But I’ll warn you right away, I’m basing my conclusions on my own axioms, not generally accepted ones. Therefore, I will start by defining mathematical operations, from which I will build a logical conclusion that will show you how to divide by zero.

Definitions:
Number and times in the text, there are synonyms in meaning.
Addition (adding) is one of the main operations (actions) in various branches of mathematics, which allows you to combine two objects (in the simplest case, two numbers).
Multiplication is an algebraic operation in which the first argument is added as many times as the second argument shows. In arithmetic, multiplication is a short notation for the sum of identical terms. For example, the notation 5*3 means “fold five times (three fives)”, that is, it is simply a short notation for 5+5+5.
You can only multiply quantity by quantity, quality by quantity, but not quality by quality. Example: 2 horses, 2 times stronger than one. Three times they took two rubles, received six rubles. You can’t take a ruble one ruble at a time.
You cannot add and multiply numbers that denote different objects, that is, you cannot add a boa constrictor with a parrot, but if you designate a boa constrictor and a parrot as an animal, you can get the sum of the animals. You can even add up a duck and a locomotive if you give them a common definition between them, such as, for example, a material body or a physical object.
Example: There were 2 ducks, 2 parrots and 2 locomotives were added to them. How many were there: a) Ducks, b) Parrots, d) Animals, c) Physical bodies?
Answer: a) 2, b) 2, d) 4, c) 6.

Division (division operation) is one https://nummuscasino.co.uk/games/ of the four simplest arithmetic operations, the inverse of multiplication. Division is an operation that results in a number (quotient) that, when multiplied by a divisor, gives the dividend.
Just as multiplication replaces repeated addition, division replaces repeated subtraction.
Example: 25\5=5, can be interpreted in 3 ways:
a) We had quality 25, we divided it by 5 times and got quality 5. That is, quality 25 consists of 5 times taken quality 5.
b) We had quality 25, we divided it into 5 qualities, received 5 times.
c) We had 25 times, we divided it by 5 times and got 5 times. That is, if we take 5 times 5 times, we get 25 times.
Times cannot be divided by quality.
Result: multiplication consists of adding a quality a certain number of times or adding times a certain number of times.
Mathematically, this can be written as follows: P*K=K, P*P=P, where P-times, K-quality.
Since division is the inverse operation of multiplication, we get: K\P=K, K\K=P, P\P=P.
Matter is what exists when nothing exists.
Nothing is that which does not exist when matter exists.
0 (zero\zero) – a number indicating:
a) as a quality – emptiness
b) as quantity – absence of an object
c) reference point
Any number other than zero means:
a) as quality – matter
b) as a quantity (times) – the presence of one type of object a certain number of times. For example: 3 would indicate that the object is present 3 times.

Since division by zero is an action that is not obvious and difficult to understand due to its specificity, in order to explain its essence, I will resort to a figurative analogy.

Imagine 3 rooms made of neither matter nor emptiness. Of course, such a substance does not exist, but this is just an image, an assumption that will allow us to build an analogy.
In the left room there is an infinite number of black billiard balls, which symbolize emptiness, which we denote by the number 0. That is, each black ball is the number 0, and you need to remember that this nothingness (0) is quality, not quantity.
In the right room there are colored balls, there are an infinite number of them, each color is a certain number, rational, irrational, positive and negative. The only ball not there is black, that is, there is no number 0. Let’s say 1 is a lilac ball, 2 is red, 5 is blue and so on… In order not to clutter the rooms, we will assume that they have a machine that produces a ball of the desired color when you enter a number. These numbers also indicate qualities. In the left room the machine produces only black balls, and in the right room any other balls except black.
The third room is completely empty, there are no balls in it. It will be our warehouse, that is, we will take balls from the first rooms and bring them to the 3rd. There is a mechanism in the room that clears it of balls.
Between the rooms there are doors through which a person can pass, who also consists of neither matter nor emptiness. He will take balls either from the left room, or from the right, or from two at once.
But before we start the experiment, we must study and understand the properties of the balls, both black and colored.
Nothing by definition is that which exists when matter does not exist.

Matter is what exists when nothing exists.
From these definitions it follows that when a black ball exists, colored balls do not exist and vice versa. Thanks to this, we have a number of interesting and unusual properties of the black ball, the essence of which will be revealed later.
A person starts from the 3rd empty room and enters either the left or right room. In an empty room, he will always bring something in his hands, either a black ball or a colored one. The 3rd room symbolizes what comes after the equal sign in mathematical equations.
And so let’s start the experiment.
The person enters the right room and takes the 1n blue ball (5) once, then he carries it into the empty room. In the 3rd room there is a blue ball. Mathematical notation for this action: 5*1=5. Let’s agree that the first number will mean quality, and the second quantity (times). The sign after equals means what is in the third room. The man cleared the room and went for the balls again, but now to the left room.
A man took 2 black balls, an unusual phenomenon happened, these balls seemed to merge into one. He took the new ball to the 3rd room. As a result, now there is a black ball there. Mathematical notation: 0*2=0. The man went to the left room a couple more times, and no matter how many times he took the black ball, in his hands it all stuck together into one black ball. In the 3rd room each time I got one black ball. Mathematical notation: 0*n=0, where n is any arbitrary number other than zero. Why is it different from zero?? Because the man decided not to take the black ball later and see what happens.
Now the man decided to take 2 black balls in the left room, they stuck together again. Then he went into the room with colored balls and took two blue balls there (5). The incredible happened – the black ball disappeared. Only 2 blue balls remained in his hands. Entering the third room, there were 2 blue balls in it. But you can mold these 2 blue ones into a 1n purple ball – 10, but you can also leave them separate. Mathematical notation: 0+5*2=10.
Then the man once again entered the room with colored balls, this time he took one yellow ball (3), 2 blue balls (5). And brought them to the 3rd room. There he decided to combine them into one, resulting in one turquoise ball 13. Mathematical notation: 3+5*2=13.
Here an interesting property of colored balls was discovered: they, like black ones, can stick together into one ball, but at the same time their color changes, and therefore their numerical value.

Mathematical expression: n*b=y, where n,b,y – any non-zero number.
Now our human experimenter decided to see what would happen if we brought a colored ball from the right room to the left. He took the blue ball 5 and brought it to the left room. For convention, let’s agree that while a ball of any color is in a person’s hands, it does not in any way affect the number of balls inside the rooms. And so a man puts a blue ball into a room where there are black balls. What’s happening? The black balls have all disappeared from the room. This happened due to the fact that the existence of matter proves the non-existence of emptiness by definition. Black balls can only exist if there are no colored balls. But colored balls, by the very fact of their existence, completely eliminate the possibility of the existence of black balls. Therefore, the man picked up a blue ball, and at that hour, black balls appeared again. And he took the blue ball into the third room, out of harm’s way. Then he cleared the room, just like previous times.
Now the man went into the blue room, looked at the blue ball, thought and thought and decided not to take it and balls of a different color too. But he needs to bring something to the 3rd room, that’s his task! Then he went to the left room and took a black ball, one, two, three, no matter how many, the main thing for him was to fulfill the condition.
In the third room, as a result, there is now a black ball. By the way, you can not only combine it into one ball, but also pull out any arbitrary number (except zero) of black balls from it. Its properties are truly amazing!
Mathematical notation: 5*0=0. In general, n*0=0, where n is any non-zero number.
Having cleared the room, the man went to do the same experiment with the left room. He looked at the black ball and decided not to take it. Then he went to the 3rd room and found that he had a black ball in his hands! But where? Doesn’t matter, he put it in the third room. Mathematical notation: 0*0=0.

But the man wondered where the ball came from? He did not take it, and then returned to the 3rd room, because according to the condition, there should always be some kind of ball in the 3rd room, initially there were no balls in it, only a person brings them there. Then where did the black ball come from??
The man cleared the room, went to the right room. I looked at the blue ball and immediately returned to 3rd. He had nothing in his hands, he didn’t take anything from the left room. He didn’t complete the task. Then he began to think, 0*0=0. Where does the ball come from if he didn’t take it?? Really from where? There’s some kind of mistake here. And then he remembered that when he left the left room, he hit his head, in a state of passion, he took one ball and entered the third room. The emotion passed, but he forgot about what he had done. It turns out, then, that he still took the ball? That’s right.
A man entered the left room. He decided not to take the black ball. But how to do it? Stop! What did he do when he didn’t take colored balls?? Walked into the next room! So, why not do the same now?? He entered the right one, and took the blue ball and took it to the 3rd. There is now one blue ball – 5. Mathematical notation: 0*0=5.
The man repeated this experiment many times, but with different balls. Every time he didn’t take the black ball, he took the colored ball. He managed to complete the task by taking an arbitrary number of balls. Mathematical notation: 0*0=n, where n is any non-zero number.

This equation follows from the definition itself: if nothing (0) exists (is not taken into the third room), then matter exists (a colored ball, that is, any number is not equal to zero). It’s simple.
0*0=0 cannot, judge for yourself, this entry is equivalent to the expression: nothing, taken never is nothing. This contradicts the previous formulas, where 0*n=0, that is, nothing taken any time, with the exception of zero, will result in nothing. This is its fundamental property. You and I noticed that a black ball can split into an infinite number of exactly the same black balls, or stick together into one black ball of the same size. Colored balls can also stick together and break up, but their color and size also change. You can split one colored ball into balls of equal size and color, but their size and color will be different from the color of the original ball. These are the properties of matter.

Now we have the equations:
0*0=n, zero as a quality (nothing) taken not once (about once) – there is any qualitative number different from zero. The same is equivalent for times: neither once nor once = once. Double negative.
n*0=0, any number different from zero (n) taken not once (0 times), is zero as a quality, that is, nothing is nothing. It’s the same with times: once never = not once.
0*n=0, zero as quality (nothing) taken an arbitrary number of times, with the exception of never, there is zero – nothing, that is, quality. It’s the same with times: not once once = not once.
Well, now the most pleasant part – division by zero!
Let me write these formulas again:
0*0=е, 0*е=0, е*0=0, where е=n (previously) is any number other than zero. Why? I like this letter, I don’t want it to disappear, so I perpetuate it this way.
We get: 0\0=е, е\0=0, 0\е=0. The result is a closed and beautiful system.

Now let’s analyze the physical meaning using an example:
6\3=2, means that 6 (quality) contains the qualities of 2 three times.
Or: 6 (quality) contains the qualities of 3 twice
6\0=0, means that 6 (quality) contains the qualities of 0 zero times.
Or: 6 (quality) contains the qualities 0 zero times.
It is logical that 6 does not consist of zeros. Since matter consists of matter, not emptiness. Emptiness in nature does not exist, like absolute. Local, perhaps, but no one has discovered it yet. Even the physical vacuum is the so-called Dirac sea, it consists of virtual particles that balance each other.
0\0=е, also makes sense. This means that zero is made up of zeros, any number of times, except never. Zero cannot consist of any number other than zero.
Yo is not a specific number, it is any number other than zero. Each equation has its own.
Here’s an example:
0=0
25 – 25 = 20 – 20
5(5 – 5) = 4(5 – 5)
5(0) = 4(0)
5*(0\0)=4*(0\0)
In this case, 0\0 on the left side is not equal to 0\0 on the right. One entry, but different results. This is right then with black balls, we can extract any number of black balls from one black ball. In this equation, 0\0 is not quality, but a designation of quantity (times), this is a simple notation. In our world there is no 0 as a quality, that is, emptiness. From the definition of what matter is. We exist in the material world. In other words, when we multiply by zero or divide by zero, we interact with times and only times, but not with quality.
0^(0)==0\0=е.
You can deduce the rest of the operations yourself.

Mathematics is a limitless science, and only thinking without limits can help you master it.