strict ban on division by zero is imposed even in junior high school.Children usually do not think about its causes, but in reality to know why something is prohibited, and it is interesting and useful.
Arithmetic
Arithmetic operations that are being studied in school, unequal in terms of mathematics.They recognize the full only two of these operations - addition and multiplication.They are part of the very concept of the number, and all other actions with the numbers one way or another are based on these two.That is, it is impossible not only division by zero, and division at all.
subtraction and division
What's missing the rest of the action?Again, the school is known that, for example, subtract from four to seven - it means to take sweets seven, four of them to eat and to count those that remain.But the math does not solve the problem of eating sweets and generally perceive them completely differently.For them there is only the addition, that is, recording 7 - 4 is a number which is the sum of the number 4 will be equal to 7. That is for mathematicians 7 - 4 - is shorthand equation: x + 4 = 7. This is not subtraction, and the task- to find a number that you need to put in place of x.
The same applies to the division and multiplication.Dividing ten to two, mladsheklassnikov lays out ten candies into two equal piles.Mathematician same here sees the equation: 2 * x = 10.
So it turns out, why not allowed division by zero: it is simply impossible.Record 6: 0 should be converted into the equation x = 0 · 6. That is, you want to find a number that can be multiplied by zero and get 6. But we know that the multiplication by zero always gives zero.This essential property of zero.
Thus, there is no number that is multiplied by zero, would give some number other than zero.So, this equation has no solution, there is no such number, which corresponds to a record of 6: 0, which means it does not make sense.On its senselessness and say that forbid division by zero.
whether zero is divided by zero?
it possible to zero divided by zero?The equation 0 · x = 0 is not difficult and can take this same x for zero and get a 0 · 0 = 0. Then 0: 0 = 0?But if, for example, taken for x unit, also received 0 · 1 = 0. It can be taken for x in general any desired number and divide by zero, and the result remains the same: 0: 0 = 9, 0: 0 = 51, and sohereinafter.
Thus, in this equation, you can insert any number of completely, and you can not select any particular, it is impossible to determine how many designated record 0: 0. That is, the record also does not make sense, and division by zero allthe same can not be: it is not divided even at himself.
This is an important feature of the division operation, that is, the multiplication and the associated number is zero.
question remains: why can not divide by zero, but it can be deducted?We can say that this mathematics begins with this interesting problem.To find the answer, you must learn the formal mathematical definitions of numerical sets and get acquainted with the operations over them.For example, there are not only simple but also complex numbers, division which differs from the conventional division.It is not included in the school curriculum, but the university lectures on mathematics begin with this.
