Why can't you divide by zero? An illustrative example. Is it possible to divide by zero? Answers mathematician Multiplying a number by 0 rule

For the first time with such an arithmetic operation as multiplication, students get acquainted on the school bench. The math teacher among the numerous rules raises the topic of "multiplying by zero." Despite the unambiguity of the wording, students have many questions. Let's look at what happens if we multiply by 0.

The rule that you cannot multiply by zero generates a lot of disputes between teachers and their students. It is important to understand that multiplication by zero is a controversial aspect due to its ambiguity.

First of all, attention is focused on the lack of a sufficient level of knowledge among secondary school students. secondary school. Crossing the threshold educational institution, participant educational process in most cases, does not think about the main goal that needs to be pursued.

During the training, the teacher covers various issues. These include the situation, what happens if you multiply by 0. In an effort to anticipate the teacher's narration, some students enter into controversy. They prove, at least they try, that multiplication by 0 is valid. But, unfortunately, this is not the case. Multiplying any number by 0 results in nothing. In some literary sources, there is even a mention that any number multiplied by zero forms a void.

Important! Attentive audience listeners immediately grasp that if the number is multiplied by 0, then the result will be 0. A different development of events can be traced in the case of those students who systematically skip classes. Inattentive or unscrupulous students are more likely than others to think about how much it will be if they multiply by zero.

As a result of the lack of knowledge on the topic, the teacher and the negligent student find themselves opposite sides contradictory situation.

The difference in views on the topic of the dispute lies in the degree of education on the subject of whether it is possible to multiply by 0 or still not. The only acceptable way out of this situation is to try to appeal to logical thinking to find the correct answer.

It is not recommended to use the following example to explain the rule. Vanya has 2 apples in her bag for a snack. At lunch he thought about putting some more apples in his briefcase. But at that moment there was not a single fruit nearby. Vanya did not put anything. In other words, he placed 0 apples to 2 apples.

In terms of arithmetic, in this example, it turns out that if 2 is multiplied by 0, then there is no void. The answer in this case is clear. For this example, the multiplication by zero rule is not relevant. The correct solution is summation. That is why the correct answer is 2 apples.

Otherwise, the teacher has no choice but to compose a series of tasks. The last measure is to re-set the passage of the topic and poll for exceptions in the multiplication.

Essence of action

It is advisable to start studying the algorithm of actions when multiplying by zero by indicating the essence of the arithmetic operation.

The essence of the action to multiply was originally determined exclusively for a natural number. If the mechanism of action is revealed, then a certain number involved in the calculation is added to itself.

It is important to consider the number of additions. Depending on this criterion, a different result is obtained. The addition of a number relative to itself determines such a property of it as naturalness.

Let's look at an example. It is necessary to multiply the number 15 by 3. When multiplied by 3, the number 15 increases three times in its value. In other words, the action looks like 15 * 3 = 15 + 15 + 15 = 45. Based on the calculation mechanism, it becomes obvious that if a number is multiplied by another natural number, there is a semblance of addition in a simplified form.

It is advisable to start the algorithm of actions when multiplying by 0 by providing a characteristic by zero.

Note! According to conventional wisdom, zero stands for the whole nothingness. For emptiness of this kind, a designation is provided in arithmetic. Despite this fact, the zero value does not carry anything.

It should be noted that such an opinion in the modern world scientific society differs from the point of view of the ancient Eastern scholars. According to the theory they held, zero was equal to infinity.

In other words, if you multiply by zero, you get a variety of options. In the zero value, scientists considered a kind of depth of the universe.

As confirmation of the possibility of multiplying by 0, mathematicians cited the following fact. If next to any natural number set to 0, then you get a value that is ten times higher than the original.

The example given is one of the arguments. In addition to proofs of this kind, there are many other examples. It is they that underlie the ongoing disputes when multiplying by emptiness.

The feasibility of trying

Among students quite often at the beginning of mastering educational material there are attempts to multiply a number by 0. Such an action is a gross mistake.

In essence, nothing will happen from such attempts, but there will be no benefit either. If you multiply by a zero value, you get an unsatisfactory mark in the diary.

The only thought that should arise when multiplying by emptiness is the impossibility of action. memorization in this case plays an important role. Having learned the rule once and for all, the student prevents the appearance of controversial situations.

As an example to be used when multiplying by zero, the following situation is allowed to be used. Sasha decided to buy apples. While she was in the supermarket, she chose 5 large ripe apples. Going to the department of dairy products, she felt that this would not be enough for her. The girl put 5 more pieces in her basket.

After thinking a little more, she took 5 more. As a result, at the checkout, Sasha got: 5 * 3 = 5 + 5 + 5 = 15 apples. If she put 5 apples only 2 times, then it would be 5 * 2 = 5 + 5 = 10. In the event that Sasha did not put 5 apples in the basket, it would be 5 * 0 = 0 + 0 + 0 + 0 + 0 = 0. In other words, buying apples 0 times means not buying any.

Which of these sums do you think can be replaced by the product?

Let's argue like this. In the first sum, the terms are the same, the number five is repeated four times. So we can replace addition with multiplication. The first factor shows which term is repeated, the second factor shows how many times this term is repeated. We replace the sum with the product.

Let's write down the solution.

In the second sum, the terms are different, so it cannot be replaced by a product. We add the terms and get the answer 17.

Let's write down the solution.

Can the product be replaced by the sum of the same terms?

Consider works.

Let's take action and draw a conclusion.

1*2=1+1=2

1*4=1+1+1+1=4

1*5=1+1+1+1+1=5

We can conclude: always the number of unit terms is equal to the number by which the unit is multiplied.

Means, multiplying the number one by any number gives the same number.

1 * a = a

Consider works.

These products cannot be replaced by a sum, since the sum cannot have one term.

The products in the second column differ from the products in the first column only in the order of the factors.

This means that the commutative multiplication property, their values ​​must also be equal to the first multiplier respectively.

Let's conclude: When any number is multiplied by the number one, the number that was multiplied is obtained.

We write this conclusion as an equality.

a * 1= a

Solve examples.

Hint: do not forget the conclusions that we made in the lesson.

Test yourself.

Now let's observe the products, where one of the factors is zero.

Consider products where the first factor is zero.

Let us replace the products with the sum of identical terms. Let's take action and draw a conclusion.

0*3=0+0+0=0

0*6=0+0+0+0+0+0=0

0*4=0+0+0+0=0

The number of zero terms is always equal to the number by which zero is multiplied.

Means, When you multiply zero by a number, you get zero.

We write this conclusion as an equality.

0 * a = 0

Consider products where the second factor is zero.

These products cannot be replaced by a sum, since the sum cannot have zero terms.

Let's compare the works and their meanings.

0*4=0

The products of the second column differ from the products of the first column only in the order of the factors.

This means that in order not to violate the commutative property of multiplication, their values ​​must also be equal to zero.

Let's conclude: Multiplying any number by zero results in zero.

We write this conclusion as an equality.

a * 0 = 0

But you can't divide by zero.

Solve examples.

Hint: don't forget the conclusions drawn in the lesson. When calculating the values ​​of the second column, be careful when determining the order of operations.

Test yourself.

Today in the lesson we got acquainted with special cases of multiplication by 0 and 1, practiced multiplying by 0 and 1.

Bibliography

1. M.I. Moro, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 1. - M .: "Enlightenment", 2012.
2. M.I. Moro, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 2. - M .: "Enlightenment", 2012.
3. M.I. Moreau. Mathematics lessons: Guidelines for teachers. Grade 3 - M.: Education, 2012.
4. Regulatory document. Monitoring and evaluation of learning outcomes. - M.: "Enlightenment", 2011.
5. "School of Russia": Programs for elementary school. - M.: "Enlightenment", 2011.
6. S.I. Volkov. Maths: Verification work. Grade 3 - M.: Education, 2012.
7. V.N. Rudnitskaya. Tests. - M.: "Exam", 2012.

1. Nsportal.ru ().
2. Prosv.ru ().
3. Do.gendocs.ru ().

Homework

1. Find the meaning of expressions.

2. Find the meaning of expressions.

3. Compare expression values.

(56-54)*1 … (78-70)*1

4. Make a task on the topic of the lesson for your comrades.

Even at school, teachers tried to hammer the simplest rule into our heads: "Any number multiplied by zero equals zero!", - but still there is a lot of controversy around him. Someone just memorized the rule and does not bother with the question “why?”. “You can’t do everything here, because at school they said so, the rule is the rule!” Someone can fill half a notebook with formulas, proving this rule or, conversely, its illogicality.

In contact with

Who is right in the end

During these disputes, both people, having opposite points of view, look at each other like a ram, and prove with all their might that they are right. Although, if you look at them from the side, you can see not one, but two rams resting against each other with their horns. The only difference between them is that one is slightly less educated than the other.

Most often, those who consider this rule to be wrong try to call for logic in this way:

I have two apples on my table, if I put zero apples to them, that is, I don’t put a single one, then my two apples will not disappear from this! The rule is illogical!

Indeed, apples will not disappear anywhere, but not because the rule is illogical, but because a slightly different equation is used here: 2 + 0 \u003d 2. So we will immediately discard such a conclusion - it is illogical, although it has the opposite goal - to call to logic.

What is multiplication

The original multiplication rule was defined only for natural numbers: multiplication is a number added to itself a certain number of times, which implies the naturalness of the number. Thus, any number with multiplication can be reduced to this equation:

1. 25x3=75
2. 25 + 25 + 25 = 75
3. 25x3 = 25 + 25 + 25

From this equation follows the conclusion, that multiplication is a simplified addition.

What is zero

Any person knows from childhood: zero is emptiness. Despite the fact that this emptiness has a designation, it does not carry anything at all. The ancient Eastern scientists thought differently - they approached the issue philosophically and drew some parallels between emptiness and infinity and saw a deep meaning in this number. After all, zero, which has the value of emptiness, standing next to any natural number, multiplies it ten times. Hence all the controversy over multiplication - this number carries so much inconsistency that it becomes difficult not to get confused. In addition, zero is constantly used to identify empty bits in decimal fractions, this is done both before and after the comma.

Is it possible to multiply by emptiness

It is possible to multiply by zero, but it is useless, because, whatever one may say, but even when multiplying negative numbers, zero will still be obtained. It is enough just to remember this simplest rule and never ask this question again. In fact, everything is simpler than it seems at first glance. There are no hidden meanings and secrets, as ancient scientists believed. The most logical explanation will be given below that this multiplication is useless, because when multiplying a number by it, the same thing will still be obtained - zero.

Going back to the very beginning, the argument about two apples, 2 times 0 looks like this:

• If you eat two apples five times, then eaten 2×5 = 2+2+2+2+2 = 10 apples
• If you eat two of them three times, then eaten 2 × 3 = 2 + 2 + 2 = 6 apples
• If you eat two apples zero times, then nothing will be eaten - 2x0 = 0x2 = 0+0 = 0

After all, eating an apple 0 times means not eating a single one. This will be clear even to the smallest child. Like it or not, 0 will come out, two or three can be replaced with absolutely any number and absolutely the same thing will come out. And to put it simply, zero is nothing and when you have there is nothing, then no matter how much you multiply - it's all the same will be zero. There is no magic, and nothing will make an apple, even if you multiply 0 by a million. This is the simplest, most understandable and logical explanation of the rule of multiplication by zero. For a person who is far from all formulas and mathematics, such an explanation will be enough for the dissonance in the head to resolve and everything to fall into place.

Division

From all of the above follows another important rule:

You can't divide by zero!

This rule, too, has been stubbornly hammered into our heads since childhood. We just know that it is impossible and that's it, without stuffing our heads with unnecessary information. If you are suddenly asked the question, for what reason it is forbidden to divide by zero, then the majority will be confused and will not be able to clearly answer the simplest question from the school curriculum, because there are not so many disputes and contradictions around this rule.

Everyone just memorized the rule and does not divide by zero, not suspecting that the answer lies on the surface. Addition, multiplication, division and subtraction are unequal, only multiplication and addition are full of the above, and all other manipulations with numbers are built from them. That is, the entry 10: 2 is an abbreviation of the equation 2 * x = 10. Therefore, the entry 10: 0 is the same abbreviation for 0 * x = 10. It turns out that division by zero is a task to find a number, multiplying by 0, you get 10 And we have already figured out that such a number does not exist, which means that this equation has no solution, and it will be a priori incorrect.

Let me tell you

To not divide by 0!

Cut 1 as you like, along,

Just don't divide by 0!

Class: 3

Presentation for the lesson

Back forward

Attention! The slide preview is for informational purposes only and may not represent the full extent of the presentation. If you are interested in this work, please download the full version.

Target:

1. Introduce special cases of multiplication with 0 and 1.
2. To consolidate the meaning of multiplication and the commutative property of multiplication, to develop computational skills.
3. Develop attention, memory, mental operations, speech, creativity, interest in mathematics.

Equipment: Slide presentation: Appendix1.

During the classes

1. Organizational moment.

Today is an unusual day for us. There are guests at the lesson. Please me, friends, guests with your successes. Open notebooks, write down the number, class work. In the margin, mark your mood at the beginning of the lesson. Slide 2.

Verbally the whole class repeats the multiplication table on the cards with speaking aloud (Children mark wrong answers with claps).

Fizkultminutka (“Brain gymnastics”, “Hat for reflection”, for breathing).

2. Statement of the learning task.

2.1. Tasks for the development of attention.

On the board and on the table, the children have a two-color picture with numbers:

– What is interesting about the written numbers? (Written in different colors; all “red” numbers are even, and “blue” are odd.)
What is the extra number? (10 is round and the rest are not; 10 is two digits and the rest are single digits; 5 is repeated twice and the rest are one at a time.)
- I will close the number 10. Is there an extra among the other numbers? (3 - he doesn't have a pair under 10, but the others do.)
– Find the sum of all “red” numbers and write it down in the red square. (30.)
– Find the sum of all the “blue” numbers and write it down in the blue square. (23.)
How much more is 30 than 23? (On 7.)
How much is 23 less than 30? (Also at 7.)
What action were you looking for? (Subtraction.) Slide 3.

2.2. Tasks for the development of memory and speech. Knowledge update.

a) - Repeat in order the words that I will name: term, term, sum, reduced, subtracted, difference. (Children try to reproduce word order.)
What action components were named? (Addition and subtraction.)
What action are you familiar with? (Multiplication, division.)
- Name the components of multiplication. (Multiplier, multiplier, product.)
What does the first multiplier mean? (Equal terms in the sum.)
What does the second multiplier mean? (The number of such terms.)

Write down the definition of multiplication.

a + a+… + a= an

b) Look at the notes. What task will you be doing?

12 + 12 + 12 + 12 + 12
33 + 33 + 33 + 33
a + a + a

(Replace sum by product.)

What will happen? (The first expression has 5 terms, each of which is equal to 12, so it is equal to 12 5. Similarly - 33 4, and 3)

c) Name the reverse operation. (Replace the product with the sum.)

– Replace the product with the sum in the expressions: 99 2. 8 4. b 3.(99 + 99, 8 + 8 + 8 + 8, b + b + b). slide 4.

d) Equations are written on the board:

81 + 81 = 81 – 2
21 3 = 21 + 22 + 23
44 + 44 + 44 + 44 = 44 + 4
17 + 17 – 17 + 17 – 17 = 17 5

Pictures are placed next to each equality.

The animals of the forest school were on a mission. Did they do it right?

Children establish that the elephant, tiger, hare and squirrel made a mistake, explain what their mistakes are. Slide 5.

e) Compare the expressions:

8 5... 5 8
5 6... 3 6
34 9… 31 2
a 3... a 2 + a

(8 5 \u003d 5 8, since the sum does not change from the rearrangement of the terms;
5 6 > 3 6, since there are 6 terms on the left and on the right, but the terms on the left are larger;
34 9 > 31 2. since there are more terms on the left and the terms themselves are larger;
a 3 \u003d a 2 + a, since there are 3 terms on the left and on the right, equal to a.)

What property of multiplication was used in the first example? (Displacement.) Slide 6.

2.3. Formulation of the problem. Goal setting.

Are equalities true? Why? (Correct, since the sum 5 + 5 + 5 = 15. Then the sum becomes one more term 5, and the sum increases by 5.)

5 3 = 15
5 4 = 20
5 5 = 25
5 6 = 30

– Continue this pattern to the right. (5 7 = 35; 5 8 = 40...)
- Continue it now to the left. (5 2 = 10; 5 1=5; 5 0 = 0.)
- What does the expression 5 1 mean? fifty? (? Problem!)

Outcome of the discussion:

However, the expressions 5 1 and 5 0 do not make sense. We can agree to consider these equalities true. But for this we need to check whether we violate the commutative property of multiplication.

So, the purpose of our lesson is determine if we can count the equalities 5 1 = 5 and 5 0 = 0 correct?

Lesson problem! Slide 7.

3. “Discovery” of new knowledge by children.

a) - Follow the steps: 1 7, 1 4, 1 5.

Children solve examples with comments in a notebook and on the board:

1 7 = 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
1 4 = 1 + 1 + 1 + 1 = 4
1 5 = 1 + 1 + 1 + 1 +1 = 5

- Make a conclusion: 1 a -? (1 a = a.) Card is exposed: 1 a = a

b) - Do the expressions 7 1, 4 1, 5 1 make sense? Why? (No, since the sum cannot have one term.)

– What should they be equal to in order not to violate the commutative property of multiplication? (7 1 must also equal 7, so 7 1 = 7.)

4 1 = 4; 5 1 = 5.

- Make a conclusion: a 1 =? (a 1 = a.)

The card is exposed: a 1 = a. The first card is superimposed on the second: a 1 \u003d 1 a \u003d a.

- Does our conclusion coincide with what we got on the numerical beam? (Yes.)
– Translate this equality into Russian. (When you multiply a number by 1 or 1 by a number, you get the same number.)
- Well done! So, we will consider: a 1 \u003d 1 a \u003d a. slide 8.

2) The case of multiplication with 0 is studied similarly. Conclusion:

- when a number is multiplied by 0 or 0 by a number, zero is obtained: a 0 \u003d 0 a \u003d 0. slide 9.
- Compare both equalities: what do 0 and 1 remind you of?

Children express their opinions. You can draw their attention to the images:

1 - “mirror”, 0 - “terrible beast” or “invisibility cap”.

Well done! So, multiplying by 1 gives the same number. (1 - “mirror”), and when multiplied by 0, we get 0 ( 0 - “invisibility cap”).

4. Physical education (for the eyes - “circle”, “up - down”, for hands - “lock”, “cams”).

5. Primary fastening.

Examples are written on the board:

23 1 =
1 89 =
0 925 =
364 1 =
156 0 =
0 1 =

Children solve them in a notebook and on a blackboard with pronunciation of the received rules in a loud speech, for example:

3 1 = 3, since when multiplying a number by 1, the same number is obtained (1 is a “mirror”), etc.

a) 145 x = 145; b) x 437 = 437.

- When multiplying 145 by an unknown number, it turned out 145. So, they multiplied by 1 x = 1. Etc.

a) 8 x = 0; b) x 1 \u003d 0.

- Multiplying 8 by an unknown number turned out to be 0. So, multiplied by 0 x \u003d 0. And so on.

6. Independent work with class validation. slide 10.

Children independently solve recorded examples. Then finished

they check their answers with pronunciation in a loud speech, mark correctly solved examples with a plus, correct the mistakes made. Those who made mistakes receive a similar task on a card and work on it individually while the class solves repetition problems.

7. Tasks for repetition. (Work in pairs). Slide 11.

a) - Do you want to know what awaits you in the future? You can find out by deciphering the record:

G – 49:7 about – 9 8 n – 9 9 in – 45:5 th – 6 6 d – 7 8 s – 24:3

81	72	5	8	36	7	72	56

"So what's in store for us?" (New Year.)

b) - “I thought of a number, subtracted 7 from it, added 15, then added 4 and got 45. What number did I think of?”

Reverse operations must be done in reverse order: 45 - 4 - 15 + 7 = 31.

8. The result of the lesson.slide 12.

What are the new rules?
What did you like? What was difficult?
Can this knowledge be applied in real life?
In the margins, you can express your mood at the end of the lesson.
Complete the self-assessment table:

I want to know more
ok but i can do better
While I'm in trouble

Thanks for your work, you did a great job!

9. Homework

pp. 72–73 Rule, No. 6.

Consider an example of multiplying an integer by zero. How much will it be if 2 (two) times 0 (zero)? Any number multiplied by zero equals zero. It doesn't matter if we know this number or not.

According to the generally accepted definition, zero is the number that separates positive numbers from negative ones on the number line. Zero is the most problematic place in mathematics that does not obey logic, and all mathematical operations with zero are based not on logic, but on generally accepted definitions.

Zero is the first digit in all standard number systems. Every month began from day zero in the Mayan calendar. It is interesting that the Maya mathematics used the same zero sign to denote infinity, the second problem of modern mathematics. Zero without a wand. absolute zero. Zero point five. Five times zero equals zero 5 x 0 = 0 See the rule for multiplying by zero above in the text. Chatyri multiply by zero for free - I answer for free that it will be zero. Free help is included - the word "four" is spelled a little differently than you write in your search query.

https://youtu.be/EGpr23Tc8iY

Where zero occurs in mathematics, logic is powerless

If you liked this post and want to know more, please help me with more content. It appeared in the comments and something hooked me. Student's question: And now, dear author, please multiply zero by zero and tell me how much you get as a result?

I have already explained in my article “What is zero” where it can be applied. You just need to take those answers that are written in textbooks: zero multiplied by zero equals zero; Dividing by zero is not allowed. Of all the foreseeable options for multiplication and division by zero, ignorant scientists have chosen the most acceptable and digestible option.

I have no problem with division by zero. I hear about the connection between Heron's formula and 0/0=1 for the first time. However, there is something impure in mathematics. Problems with raising zero to zero and negative powers. But you might as well say that 0^2 doesn't make sense either, because 0^2=0^5/0^3=0/0, and you can't divide by zero.

Zero to the zeroth power is an expression that has no meaning. Zero to the zero power is equal to one - this is how the formulas show. This amount of anything, some real, material things, can be multiplied by a number. In this case, the amount of something is expressed only by zero or a positive number.

Everything in units and in mathematics at this level is in order. This is a convention, degrees cannot be expressed in quantity, so you cannot multiply them by a number. Somewhere on this site there is Durnev with his questions on school curriculum, including mathematics. Maybe it was invented in the same way as zero? To impose certain rules and subordinate them to all other people. What only a person will not do for himself, his beloved.

It is enough that textbooks often write "belongs to the set of natural numbers" even when this is true for all numbers except complex ones. An infinite number of zeros in zero are inventions of shamans for cavemen:) If we close our eyes, then everything we look at will look the same black. Multiplication by zero must be considered from a completely different end. What is multiplication?

It is enough to understand what multiplication is, then the issue with the result of multiplication by zero will be solved by itself. 2 apples, and trying to multiply them by 0 apples, as a result, we lose our 2 apples. Apparently, those who ask this have lost at least one digit at the beginning of each number. 10 and 11 - it is appropriate to talk about percentages here.

And it’s interesting how, when dividing 0 by any number, you can subtract this number at all (even if it’s zero times) ..

It can’t be so easy to become zero from multiplication! So math is not an exact science? Someone once came up with this "rule" is not known for what. Your math is wrong. In practice, this whole mathematical topic with multiplication by 0 cannot be!!! How do you want to multiply something by 10, even by 0 - it will turn out 0 ?? Unless, of course, 0 is a black hole, or 0 as you lose, to nowhere, zero is like emptiness, nothing, but this cannot be ....

If you can’t divide something (the same 5 apples into 0 imaginary baskets), then the result of an integer number is recorded and the remainder in this division ... 0 can be multiplied many times (like I went to the forest 15 times and did not find mushrooms ...

For example, we divide 5 apples by zero people; Calculate how many times 5 degrees Celsius is greater than zero degrees Celsius. Of this, it is most likely impossible to multiply by 0 (since, by the definition of multiplication, this CANNOT be written using the addition operation) and divide 0 itself by something ... since the answer cannot be determined ...

The substitution of concepts occurs when multiplying by zero itself ... Remember, any number or operation with numbers multiplied by zero IS ANNIGATED ... In other words, the operation itself does not occur when multiplied by zero and you can simply “ignore it” ... So, you stole my idea!))) For the first time I meet a more or less clear understanding of multiplication and division by zero. Whether we consider this to be mathematical operations or not, mathematics does not give a damn.

The first example of zero being problematic is the natural numbers. In Russian schools, zero is not a natural number; in other schools, zero is a natural number. For those who are interested in the question of the origin of zero, I suggest reading the article “The History of Zero” by J. J. O’Connor and E. F. Robertson, translated by I. Yu. Osmolovsky.

At what values ​​of x is the equality true: zero multiplied by x equals zero? - this equality is true for any values ​​of x. This equality is said to have an infinite number of solutions. The math was a little easier. In the most natural way, banal typos are superimposed on my natural illiteracy when typing.

I am opposed to those sermons that mathematicians read to us and to which we all))) refer. This equation was a completely different story. Can this be or can't it be? After a little thought, I "carried out a thought experiment"))) and imagined this situation. Somewhere in the drafts all the calculations about this are lying around. You are cunning What is not accepted in wide circles is not necessarily not true.

How to spell zero or null? The words zero and zero have the same meaning, but differ in usage. Who said zero is a number? Mathematicians? 0 + 5/0… zero and five (zero) in the remainder… and then everything converges and everyone is happy… Yes, in fact, there are not so many difficulties. The problem is how to perceive Zero (as a number or as something empty) and what is meant by multiplication ...