Zero itself is a very interesting number. By itself, it means emptiness, the absence of meaning, and next to another number increases its significance by 10 times. Any numbers to the zero power always give 1. This sign was used back in the Mayan civilization, and they also denoted the concept of “beginning, reason”. Even the calendar of the Mayan people began with a zero day. And this figure is also associated with a strict ban.
Ever since the primary school years, we all clearly learned the rule "you cannot divide by zero." But if in childhood you take a lot on faith and the words of an adult rarely cause doubts, then over time, sometimes you still want to figure out the reasons, to understand why certain rules were established.
Why can't we divide by zero? I would like to get a clear logical explanation for this question. In the first grade, teachers could not do this, because in mathematics the rules are explained with the help of equations, and at that age we had no idea what it was. And now it's time to figure it out and get a clear logical explanation of whycannot be divided by zero.
The fact is that in mathematics only two of the four basic operations (+, -, x, /) with numbers are recognized as independent: multiplication and addition. The rest of the operations are considered to be derivatives. Consider a simple example.
Tell me, how much will it be if 18 is subtracted from 20? Naturally, the answer immediately arises in our head: it will be 2. And how did we come to such a result? To some, this question will seem strange - after all, everything is clear that it will turn out 2, someone will explain that he took 18 from 20 kopecks and he got two kopecks. Logically, all these answers are not in doubt, but from the point of view of mathematics, this problem should be solved differently. Let us recall once again that the main operations in mathematics are multiplication and addition, and therefore, in our case, the answer lies in solving the following equation: x + 18=20. From which it follows that x=20 - 18, x=2. It would seem, why paint everything in such detail? After all, everything is so simple. However, without this it is difficult to explain why you cannot divide by zero.
Now let's see what happens if we wish to divide 18 by zero. Let's make the equation again: 18: 0=x. Since the division operation is a derivative of the multiplication procedure, then by transforming our equation we get x0=18. This is where the impasse begins. Any number in place of x when multiplied by zero will give 0 and we will not be able to get 18. Now it becomes extremely clear why you cannot divide by zero. Zero itself can be divided by any number, but vice versa -alas, no way.
What happens if zero is divided by itself? It can be written like this: 0: 0=x, or x0=0. This equation has an infinite number of solutions. So the end result is infinity. Therefore, the operation of division by zero also makes no sense in this case.
Division by 0 is at the root of many imaginary mathematical jokes, which, if desired, can puzzle any ignorant person. For example, consider the equation: 4x - 20 \u003d 7x - 35. We will take 4 out of brackets on the left side, and 7 on the right. We get: 4(x - 5) u003d 7(x - 5). Now we multiply the left and right sides of the equation by the fraction 1 / (x - 5). The equation will take the following form: 4(x - 5) / (x - 5) u003d 7(x - 5) / (x - 5). We reduce the fractions by (x - 5) and we get that 4 \u003d 7. From this we can conclude that 22 \u003d 7! Of course, the catch here is that the root of the equation is 5 and it was impossible to reduce fractions, since this led to division by zero. Therefore, when reducing fractions, you must always check that zero does not accidentally end up in the denominator, otherwise the result will turn out to be completely unpredictable.
