Zero itself is a very interesting figure.Itself is emptiness, the absence of values, and next to another figure increases its importance in 10 times.Any number in the zero degree always give 1. This sign was used even in the Mayan civilization, and it is they still stood for the notion of "the beginning of the reason."Even at the Mayan calendar began with the zero-day.And this figure is associated with a strict ban.
since elementary school years, we have clearly learned the rule "can not divide by zero."But if a child is seen by many in the faith and the words of the adult is rarely in doubt, in time sometimes you still understand the causes, to understand why they have been set or other rules.
Why can not divide by zero?On this question I want to get clear logical explanation.In first grade teacher could not do it, because in mathematics rules are explained with the help of equations, and at that age, we had no idea what it is.And now it's time to find out and get a clear logical explanation as to why you can not divide by zero.
fact that in mathematics, only two of the four main operators (+, -, x, /) with a number of recognized independent: multiplication and addition.The rest of the operation is considered to be derived.Consider a simple example.
Tell me how much you get when you subtract 18 from 20?Naturally, in our head there immediately answer: it is 2. And as we come to this result?To some, this question may seem strange - after all, everything is clear what will happen 2, someone will explain that between 20 cents and 18 took him to get two kopecks.Logically, all these answers are clear, but from the point of view of mathematics to solve this problem should be different.Again, that the main operations in mathematics are addition and multiplication, and so in this 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 do so in detail about it?After all, everything is just elementary.However, without it hard to explain why you can not divide by zero.
Now let's see what happens if we wish 18 to divide by zero.Again, we form the equation: 18: 0 = x.Since the operation of division is derived from the multiplication of procedures, it transformed our equation we get x * 0 = 18. Here is just a dead end begins.Any number of Xs in place when multiplied by zero gives 0 and get 18, we did not succeed.Now it becomes very clear why you can not divide by zero.Zero itself can be divided into any number you want, but on the contrary - alas, no way.
And what happens if a zero divided by myself?It can be written in the form: 0: 0 = x or x * 0 = 0. This equation has an infinite number of solutions.Therefore, the result is infinity.Therefore, the operation of division by zero, and in this case, too, has no meaning.
Division by 0 is at the root of many imaginary mathematical jokes that if you want you can puzzle any ignorant person.For example, consider the equation: 4 * x - 20 = 7 * x - 35 taken out of the brackets on the left side 4, and 7. The right will receive: 4 (x - 5) = 7 (x - 5).Now multiply the left and right side of the equation by a fraction 1 / (x - 5).The equation will look like this: 4 (x - 5) / (x - 5) = 7 (x - 5) / (x - 5).Will reduce the fraction by (x - 5), and we leave that 4 = 7. From this we can conclude that the 2 * 2 = 7!Of course, the catch here is that the root of the equation is equal to 5, and reduce fractions was impossible, since it led to the division by zero.Therefore, while reducing fractions should always check to zero accidentally ended up in the denominator, otherwise the result will be quite unpredictable.
