Zero itself is a very interesting figure. By itself means emptiness, lack of meaning, and next to another figure increases its significance by a factor of 10. Any number in the zero degree always gives 1. This sign was used even in the Mayan civilization, and they still denoted the concept of "beginning, reason". Even the calendar of the Mayan people began from the zero day. And this figure is connected with a strict ban.
Since the early school years, we have clearly learned the rule "you can not divide by zero". But if in childhood you perceive a lot on faith and the words of an adult rarely cause doubts, then in time you sometimes want to understand the reasons, understand why these or other rules were established.
Why can not you divide by zero? On this question I want to get an understandable logical explanation. In the first class, teachers could not do this, because in mathematics 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 sort it out and get an understandable logical explanation of why you can not divide 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 remaining operations are considered to be derivatives. Let us consider a simple example.
Tell me, how much will it be if 20 is taken away from 18? Naturally, in our head there is an instant response: it will be 2. And how did we come to this result? Someone will find this question strange, because everything is clear that it will turn out 2, someone will explain that he took 18 kopecks from 18 kopecks and he got two kopecks. Logically, all these answers are unquestionable, but from the mathematical point of view, this task should be handled 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 the solution of the following equation: x + 18 = 20. From which also it follows that x = 20 - 18, x = 2. It would seem, why should I paint everything in such detail? After all, everything is elementary simply. However, without this, it's hard to explain why you can not divide by zero.
And now let's see what happens if we wish 18 to divide by zero. Again, write the equation: 18: 0 = x. Since the operation of division is a derivative of the multiplication procedure, then by transforming our equation we obtain x * 0 = 18. This is where the dead end 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 can not divide by zero. Zero itself can be divided into any number, but on the contrary - alas, you can not.
And what happens if you divide the zero into yourself? This can be written in this form: 0: 0 = x, or x * 0 = 0. This equation has an infinite number of solutions. Therefore, as a result, infinity is obtained. Therefore, the operation of dividing by zero and in this case also does not make sense.
The division into 0 lies at the root of many imaginary mathematical jokes, which if desired can puzzle any ignorant person. For example, consider the equation: 4 * x - 20 = 7 * x - 35. We take out the brackets in the left part 4, and in the right 7. Let's get: 4 * (x - 5) = 7 * (x - 5). Now we multiply the left and right sides of the equation by the fraction 1 / (x - 5). The equation takes the form: 4 * (x - 5) / (x - 5) = 7 * (x - 5) / (x - 5). We cut the fraction by (x - 5) and we will get that 4 = 7. From this we can conclude that 2 * 2 = 7! Of course, the trick here is that the root of the equation is 5 and it was not possible to reduce the fraction, since this led to division by zero. Therefore, if you reduce the fractions, you should always check that zero is not accidentally found in the denominator, otherwise the result will be completely unpredictable.