Showing posts with label zero. Show all posts
Showing posts with label zero. Show all posts


Multiplication by zero and zero element

Mathematicians claim that when multiplied by zero, multiplication occurs and "multiplying by zero (zero element) gives a number equal to zero." Let's look at a couple of examples.

Zero on the football field

We go to the stadium to watch European football. This is exactly what blondes need. Firstly, beautiful gerls are shown on TV. Secondly, in European football, twenty-two millionaires kick the same ball with varying degrees of success. Where else will blondes find so many rich suitors in one place? And so, the game is in full swing. One player has broken the rules and is removed from the field. What is left on the field instead of this player? An empty space that cannot take part in the game. If the players are numbers, then the empty space is zero. Empty space is not a player, zero is not a number.

Now consider the "null element", which is no different from the "numeric elements". The same football match, the same situation - the player was sent off. And here is the main trick - instead of a remote player, a "zero player" with the number "zero" on a T-shirt enters the field. He joins the game and soon scores a goal. This is where "higher mathematics" begins. One team proves that the zero player is exactly the same as the rest of the players, therefore, has the right to score goals. The other team proves that this is a removed player and he does not have the right to score goals. Here's a great excuse for you to start a "special military operation" like a "football war" between El Salvador and Honduras in 1969. The idiocy of such a situation needs no comment.

Multiplication by zero in the store

Zero dollars. Mathematics For Blondes.
Zero dollars

Another example from our life. We all go to the store and buy something. What is the buying process? This is the exchange of the money we have for the goods available in the store. The buying process itself can be compared to multiplication. If the buyer has money, and the store has goods, there are no problems. If the customer doesn't have the money or the store doesn't have the product, then you can't make the purchase. You wouldn’t go to the store with an empty wallet to hear from the seller that you can’t buy anything without money? This situation can be seen as an example of multiplication by zero.

Now consider the process of buying with "zero element". Imagine that you have a bill in your wallet that says "zero dollars". You go to the store with this bill and exchange it for a piece of paper with the inscription "zero goods". Technically, you made a purchase without having a cent in your pocket and without buying anything. Mathematicians tell us about a similar “multiplication by zero (zero element)”.

Multiplication by zero is not possible

The substitution of concepts can change our logic beyond recognition. This modified logic forces us to look for multiplication by zero where it cannot be - in the results of multiplication. Since multiplication by zero does not occur, then you need to look not into the void (after all, there is no result of multiplication by zero), but into the initial conditions of multiplication. Two apples both lay and will remain lying, even after casting the spell "Apples, I multiply you by zero." Mathematically, this is written to the point of banality simply:


All this happens because our mathematicians have not learned to adequately describe reality with the help of mathematics. If you want to look at multiplication examples taken from real life, then you can do it here.

We will consider multiplication by zero in geometry and physics in more detail, to be continued.

P.S. What should you do? Remember that zero is not a number. And when it comes to zero in mathematics, discard your logic and common sense and open the Holy Mathematical Scripture. What is written about the case you are interested in, then tell the mathematicians. You will not begin to assert in a theological seminary that there is no God. So I do not recommend arguing with mathematicians - this is fraught with serious consequences for you. When you become adults and mathematicians disappear from your life, then you can say what you think is right.


Multiplication by zero

In the comments to the article "Multiplication by zero" of the Russian version of this site, I was asked an interesting question:

Nikolai, I read the article halfway, but still ... There are two apples in front of me (fact). Further, I, like a "sorcerer", multiply them by zero and still see two apples in front of me! Although, according to the laws of arithmetic, they should have disappeared from me! What does mathematics say about this? Thanks for the answer.

Two apples. Mathematics For Blondes.
Two apples

Here they are, beauties. They lie down and smile. Like, well, what do you say to that? So what is multiplication by zero? Let's try to figure this out.

Pay attention, the question is formulated very cleverly: not "what do mathematicians say?", but "what does mathematics say?". The first question is the easiest to answer. Preachers say, "Read the Bible," mathematicians say, "Read the Definition." They answer stupidly. Nobody needs to explain anything. And the meticulous can always, with a smart look, hang noodles on their ears.

Next, we will consider the situation from the position of the "sorcerer". The sorcerer declares that he will multiply the apples by zero. Then the sorcerer says: "Close your eyes and do not open." While your eyes are closed, the sorcerer hides the apples. "Open your eyes. See the apples? They are not there. The great miracle of multiplication by zero has happened - the apples have disappeared!" The sorcerer-mathematician will surely add: "What was required to be proved."

Now a few words about mathematicians. They, like proud eagles, soar high in the clouds of their abstract ideas. Mathematicians descend to our sinful earth only when they see food - a problem that they can solve. Mathematicians have learned very well to tear numbers from reality and perform various manipulations with them. When it becomes necessary to bring numbers back to reality, sometimes very big problems arise. Multiplying by zero is one such problem.

Let's start from the very beginning. The Russian-language Wikipedia page in one of the versions wrote: "Multiplication is one of the main binary mathematical operations (arithmetic operations) of two arguments (multiplicand and multiplier), the result of which is a new number (product). ... Multiplication by zero (zero element) gives a number equal to zero: x ⋅ 0 = 0".

If we translate the above quote into ordinary human language, then two elements (multiplicand and multiplier) are needed for multiplication. After multiplying them, a new element will be obtained, which is the result of multiplication. It is customary to write it like this:


On the left side of the equal sign is written what precedes the multiplication. The result of the multiplication is written on the right side. One element is multiplied by another element, resulting in a third element.

If we consider the logic of mathematicians, then calling zero the "zero element", all the "laws" of multiplication are observed - when multiplied by the zero element, all other elements turn into the zero element. There is only one question left: "Where do the apples go?".

Now I will present my own view on the problem of multiplication by zero. First read my reasoning, and at the end I will give practical recommendations on how to use my new knowledge. So what does the math say about multiplying by zero?

From the point of view of mathematics, multiplication by zero is impossible, since the multiplication itself does not occur. If in my earlier works I stated something else, then I was mistaken. The process of cognition is continuous and what seemed right to me yesterday may look completely different today.

The positional notation of numbers looks like this: units, tens, hundreds... If there is a number in the positional notation, then we write it down. For example, 324 is three hundred, two tens, four ones. And if there is no number in a separate position? What then? We write zero instead of the number that is missing. For example, 304 is three hundred, no tens, four units. I affirm that the absence of a number cannot be a number. In other words, zero is not a number and the rules of numbers do not apply to it.

In the multiplication example, zero represents an empty space in the place of one of the factors and an empty space in the result of the multiplication. Multiplication, as a mathematical operation, does not occur. It's like trying to clap with one hand. To get sound, there must be two palms. You see how smart we have become: we have determined that clapping is a binary operation that can be described by the mathematical operation of multiplication:

[one palm]*[other palm]=[applause]

Do you want to add numbers here? Please:


Now let's remove one palm. In our mathematical expression, we will replace one of the palms with zero and look at the result.



In order for the multiplication to occur, we need two completely different palms, and not the same one. Mathematicians tell us that when a number is raised to the second power, it multiplies itself. It is just as impossible to multiply a number by itself as it is impossible to create an applause with one palm.

You can say that in audio equipment, one speaker can produce sound, the second speaker is not needed for this. In the case of a speaker, there is another multiplication formula: the speaker is multiplied by the electric current and the result of the multiplication is sound.

1[speaker]*1[electric current]=1[sound]

If there is no speaker (for example, it is broken), the electric current cannot produce sound.

0[speaker]*1[electric current]=0[sound]

If there is no electric current (Putin cut off the wires), the speaker cannot produce sound.

1[speaker]*0[electric current]=0[sound]

In ordinary human language, the operation of multiplication by zero can be translated as follows:


Multiplication does not occur because there is nothing to multiply, the result of multiplication is absent.


Multiplication does not occur because there is nothing to multiply by, the result of multiplication is absent.

Something like this. Next time I will tell you about the zero element in multiplication.


2 to the power zero five

How much is 2 to the power zero five? A trick question, like everything mathematicians come up with for us. In short, transformations look like this.

2 to the power zero five. Square root of 2. Mathematics For Blondes.
2 to the power zero five

  Now let's take a closer look at the logic of mathematicians. Raising a number to an integer power is the multiplication of these numbers. Raising a number to a fractional power is extracting the root of a number, with the number in the denominator showing which root to find. But the fraction itself can be written both in the form of a decimal fraction, and in the form of a regular fraction. We put all this in a pot, mix thoroughly and the mathematical puzzle for the textbook is ready.


 You need to solve this puzzle in the following order. We convert the decimal fraction zero five into a regular fraction and get one second. Now we can write the number 2 with a fractional exponent as the square root of two and calculate its value.


To consolidate knowledge, consider two more simple examples. 


4 to the power zero five. Square root of 4. Mathematics For Blondes.
4 to the power zero five

4 to the power zero five is the same as 4 to the one-second power. Four to the power of one second is the square root of 4. Taking the square root of four gives two.


25 to the power zero five. Square root of 25. Mathematics For Blondes.
25 to the power zero five

After considering the two previous examples, it will be very easy to calculate 25 to the power zero five. As real shamans, we turn zero five into one second, extract the square root of 25 and get the desired result - the root of twenty-five is five. 


Why all these dances of shamans with tambourines? There are two sides to this math medal. Front side - mathematicians teach us to use mathematics. The other side of the coin is that if mathematicians simply and clearly express their thoughts in the language of mathematics, then they will not seem so smart to us, and we ourselves will not look such fools.



In Wikipedia there is a page of a trapezoid. In the drawing it is shown that any trapezoid can be turned into a rectangle.

Trapezoid. Mathematics For Blondes.
Let's look at algebra. These are formulas for calculation of lengths of diagonals of a trapezoid.

Diagonals of trapezoid. Mathematics For Blondes.
Diagonals of trapezoid
We substitute in these formulas data for a rectangle.

Diagonals of rectangle. Mathematics For Blondes.
Diagonals of rectangle
If to trust these formulas, the rectangle has no diagonals. Even schoolboys or schoolgirls can make what mathematicians couldn't make – to execute verification of the solution of a task. It is the actual level of modern mathematics – any statement of mathematicians can be false.

Height of a trapezoid

Height of a trapezoid is determined by the area of a triangle. The area of a triangle is calculated on Heron's formula. The sizes of the parties of a trapezoid allow to receive a triangle which has the same height as a trapezjid. The cunning trick of mathematicians allows to calculate length of diagonals of a trapezoid.

Height of a trapezoid. Mathematics For Blondes.
Height of a trapezoid
 When the legs of a trapezoid are parallel, the triangle disappears and the cunning trick ceases to work. If to determine height of a trapezoid by the area of a trapezoid, then no problems arise upon transition to a rectangle or a parallelogram.

Height of a rectangle. Mathematics For Blondes.
Height of a rectangle
 Conclusion: cunning tricks of mathematicians can result in false results.


Zero and infinity

Subject of occupations:
Subject of the previous lesson
Distinctions between multiplication and addition

Lesson 11

Zero and infinity

If the angle is equal to zero or 90°, then the two dimensional rectangle disappears and there is a one-dimensional piece. From here the sense of infinity follows: as if we did not change the party of a rectangle, it will never turn into a piece. Unit divided into zero is not equal to infinity. Infinitesimal size is not equal to unit divided into infinity.

Zero and infinity. Mathematics For Blondes.
Zero and infinity

Difference between elements in these inequalities same as difference between the point lying on a straight line and the point which is not lying on a straight line.

Multiplication to zero and division by zero do not fall into to mathematical operations with numbers, they are carried out in the field of units of measure. It is possible to call these values of trigonometric functions non-numerical.

In addition to the materials about multiplication and division by zero explained earlier it is necessary to add the following. In positional notation zero designates lack of number of the particular category. Lack of number number cannot be. Here zero is similar to punctuation marks in writing which have the graphic form, but are not said when reading.

Generally zero should be understood as lack of the considered unit of measure. For example, zero value of a angle means that the angle is absent. Division by zero should be considered as need of introduction of a unit of measure, perpendicular to already existing, for the further solution of a task. Division by zero does not mean automatic transition to multiplication. For example, it is impossible to describe turn of a piece in one-dimensional space, for this purpose it is necessary to enter padding measurement and to consider a task in two dimensional space.

At the following lesson we will consider
Decomposition on factors


The problem about the juice

The problem about the juice. Mathematics For Blondes
The problem about the juice
 On the Internet there are a lot of things. Yesterday I saw an interesting problem about the juice. I understand that the person made a mistake copying the text of the problem from the book. But it turned out very interesting. I used to see all over the math, just as I am translating the language of mathematics to the surrounding reality. That's how I read this problem and this is the decision I did.

A liter of grape juice is worth 6 manat. It was mixed with a liter of mulberry juice manat. A liter of juice sold for 10 manats. What benefits can be obtained from the sale of 10 liters of the mixed juice?

For those other than dollars knows nothing, to announce that manat - is the monetary unit of Azerbaijan (there is such a country). By the way, Muslims do not eat pork, mathematicians so do not use math-degree measure of angles in Calculus. As they say, find ten differences. It was the information for the overall development, but will return to the problem about the juice.

The number in the value of mulberry juice available. The man forgot to write. But mulberry juice can be stolen. Then it really does not cost anything. Such "schemes" are thriving in our lives. The lack of numbers in mathematics to denote the numeral zero. If we substitute the value of zero in mulberry juice, then the problem is easily solved.

For a start, we determine the number of cocktail, which is obtained by mixing two different juices. Each juice we take in the amount of one liter. If you do not like liters, take one gallon.

1 + 1 = 2 liters

Now we consider the cost of the resulting cocktail

6 + 0 = 6 manats

Calculate the cost per liter of cocktail

6: 2 = 3 manats

Who is the most interesting point - we determine the profit from the sale of a liter of cocktail

10 - 3 = 7 manats

At the end of the general view of the profits from this scam

10 * 7 = 70 manats


1. With revenues of these scams is not to compare, but enough to start.
2. The juice can be diluted with water, then stealing nothing.


1. For the theft could be imprisoned.
2. For juice dilution with water can beat face.

If in the problem still listed price for mulberry juice, instead of the zero substitute that number. The solution of the problem will not change. Incidentally, the legal business from the business of the criminal also a little different.


Division by zero in physics

Switch. Dividing by a zero in physics. Example of application of mathematics. Mathematics for blondes. Mathforblondes.
All laws can be divided into two groups - invented by us and the laws of mathematics. Laws invented by us may not work in spite of the fact that we invented them. The laws of mathematics, which are displaying the laws of nature, always work, regardless of whether we know them or do not know. That is the case with the law of multiplication and division by zero.

There is an old student's joke that the device that performs mathematical operations of multiplication and division by zero is an ordinary switch. Personally, I more trust the not fresh views of students, than the "scientific" opus of different "scientists". Usually, the first impression is correct.

All mathematical letups, that were written here, I deleted at first, because I believed that the harm from them will be more than good. Comments I cleaned similarly. But then changed my mind. If I will not tell about mathematical principles of work of electric switch, then others will not soon do it. And so, to begin a comment (to the page in Russian language):

"Idiot, Ohm's law correctly write down. Why is current is not equal to zero at zero voltage? And why does a resistance of burned out bulb is zero? You're either blind or can not to read. All is excellent divided by zero when you know the function of dependence. In most cases, the result is infinity. And about the real uncertainties you, probably, did not hear in general. I'm not going to talk about all the options, where it will not work. Even if not to pay attention to the serious errors in the examples. So I conclude you don't have a brain."

This is a typical reaction of a person to coach at zero, as a trained dog on a command "Attack!". It is thus needed to remember that the math is considering abstract concepts that aren't to need understood. In the result, we all turn into trained animals who think exactly as they were taught. I know from own experience how hard it is to get rid from the generally accepted stereotypes. So I explain that throughout the following discussion I will talk not about numerical values of physical quantities, and about the units, which are usually not considered in general mathematics.

Each of us in our daily lives every day many times uses multiplication and division by zero. Engineers, as well as we, suspecting nothing, created a special device that allows to multiply and divide by zero. And all of this is so firmly established in our lives, that without these devices is impossible to imagine our life around. But let's begin one after another, from the math.

All of you know the mathematical law of multiplication:

a*b = c

On the pages of this web-site I told about the mathematical rules of multiplication and division by zero. Take from this page these formulas, which we will use:

ab*0 = 0 and a or b

a/0 = ab

We will rewrite these formulas in a that kind, in what we will use them in our concrete example:

a*b*0 = (a*0)*b = a*(b*0) = c*0

c*0 = {c=0; a=0; b≠0} = {c=0; a≠0; b=0}

a/0 = b/0 = a*b = c

Now we'll check how these algebraic letups correspond to reality. For this, we represent the most ordinary domestic situation: you're sitting in the evening in the livingroom and suddenly light shuts off. What is your first thought? Correctly, either electricity disappeared or a bulb burned out. Or if trying is possible to think of two others variants: either you suddenly became blind or you suddenly died. Since the latter two options are more to biology, we do not consider they. But as far as exactly the first two variants can be described by our algebraic formulas, let's look.

Luminescence of bulb in physics is described by the Ohm's law that looks so:

I*R = U

In this kind the Ohm's law fully coincides the law of increase presented by us in an algebraic kind:

a*b = c

According to this, in the further reasoning, we can replace the algebraic elements of formulas by physical quantities:

a = I - it is a current that flows on wires, it is measured in Amperes;

b = R - it is a resistance to the electric current is in the spiral of bulb, it is measured in Ohms;

c = U - it is a voltage in an electrical circuit, that compels a bulb to shine, it is measured in Volts.

The first variant of the apocalyptic gloom involves to shutdown of knife-switch by some evil man (for to save energy but without our consent), as a result an electric current stops to enter on wires. Or broken wire in an accident on electrical networks.

U*0 = {U=0; I=0; R≠0}

As we see, this mathematical result reports us, that a bulb really left off to burn, as an electric current disappeared in wires, but with our bulb all is normal and she is ready again to begin to shine, as soon as a current will appear.

Now we will look at the second variant of total eclipse, when a bulb simply burned out for us, and with a current in electric networks all is normal:

U*0 = {U=0; I≠0; R=0}

As see, unlike traditional "any number increased on a zero equals a zero", we got establishment of fact of extinct bulb not only U=0, but also two possible reasons of this annoying incident : {I=0; R≠0} and {I≠0; R=0}.

It is here needed to mark that in traditional mathematics multiplying by a zero what or element of equality taken to one of basic mathematical equalities:


Usually all mathematics closes thereon. In the variant of multiplying offered by me by a zero this situation means disappearance of primary equality and passing to two inequalities - tension is not equal to strength of current and tension is not equal to resistance of electric chain :

U ≠ I

U ≠ R

In a general view for algebraic expression a*b = c it looks so:

c ≠ a

c ≠ b

For renewal of primary equality it is necessary to execute the mathematical operation of dividing by a zero. In our example it is necessary either to recover an electric current in wires or replace a burneout bulb. Thus there is the following:

I/0 = [I*(R*0)]/0 = I*(R*0/0) = I*(R*1) = I*R = U

R/0 = [(I*0)*R]/0 = (I*0/0)*R = (I*1)*R = I*R = U

Equality is used in our case 0/0=1, where as unit units come forward electric that or electric resistance. Introduction to the formula of any other unit of measuring will not result in a primary result, as electric tension ensues exceptionally co-operation of strength of current and resistance. you can go about in circles, winding meters long and почесывая itself in the back of head. You can get a purse and throw about money. Burneout bulb from it will not begin to shine:

I/0 = [I*(L*0)]/0 = I*(L*0/0) = I*(L*1) = I*L ≠ U

I/0 = [I*($*0)]/0 = I*($*0/0) = I*($*1) = I*$ ≠ U

As see, application of dividing by a zero supposes the presence of reason, but not dull implementation of mathematical actions.

In conclusion I want to say that engineers did switches allowing to execute multiplying and dividing by a zero in electric chains already a long ago. This device is basic custom control by electric chains. Switches are equip practically all electric devices: bulbs, engines, televisions, mobile telephones and other.


Why is a zero not a number?

Why is a zero not a number? Let us conduct a scientific experiment. We will take any number and will execute the simplest mathematical action - addition or deduction.

Simply so to execute a mathematical action will not turn out. One number and one sign of mathematical action are simply two mathematical symbols, standing alongside. Single character designates a number, the second symbol designates an action.

7 +
7 –

In order that an action happened, it is needed yet something. Only then we will get a result. And this result depends on that we take exactly. If we will take other any number, then the first number will change. The result of this change we write down after equal sign.

7 + 2 = 9
7 – 2 = 5

number + number = result
number - number = result

And that will be, if we will take a not number? For example, will we add salt, will add a paint, will decrease a temperature? That will be with a number, if to salt him? Nothing. A number will remain unchanging.

7 + salt = 7

Now we will try to paint a number.

7 + paint = 7

A number did not change again. But as regarding that, to push in our number in a refrigerator and lower his temperature?

7 - temperature = 7

Why does take place so? Because salt, paint, temperature numbers it is not been. A number and not number inter se do not co-operate. If to take them and make an effort with them to do anything, for us nothing will turn out. What number we took at the beginning, the same we get in the end.

number + not number = number and not number
number - not number = number and not number

Mathematicians and philosophers will argue that a number is an abstract concept that does not exist in the wild, and salt, paint, temperature, is the real things. Exactly from a difference abstract and real nothing takes place. The abstract can not influence on the real, real can not influence on abstract. What, I fully agree with the conclusions of mathematicians and philosophers. They are absolutely right - for a change real the real is needed, for a change abstract the abstract is needed.

In the second part of our experiment we will try to the abstract number to add anything abstract. Well, for example, soul. In hands this thing nobody held, she is not fixed scientific devices. The soul is this cleanly abstract concept. We will look at a result.

7 + the soul = 7
7 - the soul = 7

As see, even many abstract concepts are not able to run the number, because not all abstract concepts are numbers.

Here time to conduct an experiment with a zero, the same abstract concept, as well as number came now. We will add and will take away a zero from a number and will look at a result.

7 + 0 = 7
7 – 0 = 7

As a result of addition or deduction of zero a number remains unchanging. And takes place so because zero, as well as all other not numbers, a number is not. A zero does not possess all those properties that is possessed by numbers.

For plenitude of the conducted experiment it is needed to consider the mathematical operations of increase and division. Multiplying and dividing by a zero in mathematics has a result different from the originally taken number. But let us remember history of development of mathematics.

Addition and deduction appeared at first, an increase and division appeared then. Probably, somewhere a zero appeared after it. There was it in those times, when a faith in God was basis of existence of man. About no results of experiments there could not be speech, if these results conflicted with a faith. Here on this faith and the results of increase and dividing are founded by a zero. Someone said that a zero was a number and in it believed. Someone offered the result of multiplying by a zero - believed in a result. In him we are pin faiths until now: any number increased on a zero equals a zero.

With dividing by a zero there were problems. Nobody was able to offer nothing clever, such, that all believed in it. Mathematical experiments with the results of dividing by a zero give contradictory results and trench upon bases of mathematics. A compromise variant was therefore found is a phrase, "dividing by a zero is impossible". It did not mix to believe that a zero is a number, and did not result in the necessity of revision of other substantive provisions of mathematics. Absence of result of division of number on a zero confirms circumstance that in this case we deal with a not number.



Mathematics forever!

Mathematics forever!

You can congratulate me, my first scientific publication went out in light. There are "The papers of independent authors" in a magazine, producing № 18, to the page 110 the little article is printed under the modest name "About symmetry of mathematical actions".

At the last time (in a blog in Russian language) I promised you to show that needs to be done in order that impossible in mathematics became possible. In this little article, only on two pages of text, it is shown, as a commutative law works at deduction and division. If someone wants to look, can pass on this page (in Russian language), there is reference for a flush-off. Nothing difficult in this article is present - the half of text is occupied by examples on addition, deduction, increase and division. All at the level of middle classes of school. Such mathematics any blonde will understand.

Here so, unnoticed, we with you began to live in a completely another epoch - Epoch of Great Mathematical Opening. Doing these mathematical opening coming to you, I can only broadly speaking explain to you, what mathematics, where in mathematics, opening is hidden and as they need to be searched. By the way, my article is the first step on a way to dividing by a zero. Mathematical actions are symmetric: if in mathematics there is multiplying by a zero, means there is under an obligation to be dividing by a zero. If dividing by a zero is impossible, means multiplying is impossible by a zero. The third variant (that is known by us all) can not be. When I will show you, where and as there is dividing by a zero, you will understand that mathematics is this not паханное field on that we engage in the most primitive collector. To throw open and take the crop on the mathematical field, at a desire, any of you can.


Division by zero - the question formulation

Division by zero is maybe - to such conclusion we have come. But to solve a problem about division of number into a zero we and could not. Then let's solve not a specific target on division of number into a zero, and a zero problem as a whole. We begin all from the very beginning.

What is the zero? All-knowing Wikipedia says that the zero is a number. This number designates a point on a numerical straight line which separates positive numbers from the negative. Give also we will look at this well-known numerical straight line in which the dog on a nickname "Zero" is buried.

Number line. Mathematics for blondes.
Number line
And now we will look, as the zero in the basic mathematical operations behaves agrees the standard mathematical rules:

a + 0 = a

0 + a = a

a - 0 = a

0 - a = -a

a - a = 0

a · 0 = 0

a : 0 = ?

0 : a = 0

0 : 0 = ?

In that mathematicians are mistaken, including division into a zero impossible, we have already understood. Instead of whether and mathematicians are mistaken in other places at the formulation of results of mathematical actions with zero? Quite probably that some from resulted above equalities are false statements.

The problem with zero in the mathematician dares simply and gracefully, in style of blondes. Therefore mathematicians to such never will guess. Here the sober and critical sight of the person from outside, without fanatical belief in the received mathematical knowledge is necessary. Blondes for a zero solution of a problem approach as well as possible. About the mathematician they have the most general representations. Their mentality differs from the standard.

Whether you can find a solution of a problem with zero? The variants of the decision leave in comments.


Division of number into a zero

Last time we have considered possibility of division into a zero, and have come to conclusion that Division by zero is maybe. But it was only the half of a problem of division into a zero which decision we undertook. There is one more set of the equations of division into a zero which we are simply obliged to consider.

We have very cheerfully laughed over Wikipedia, now has come turn of all of the others to laugh over us. We will try to answer on a question that will turn out if to try to divide any number into a zero. That the number as a result cannot turn out, we have neatly noticed. Then, what can turn out? Not clearly that. We will designate it "not clearly that" which turns out as a result of division of number into a zero, a question mark. At us such small set of the mathematical equations will turn out:

a : 0 = ?

0 · ? = a

a : ? = 0

Now the equations received from the equation of division of number on a zero, we will try to sound and compare to the rules accepted in the mathematician. If a zero to divide on not clear that, any number as a result will turn out. As we know from the previous message, it is possible to assume only that any number turns out as a result of division of zero into a zero.

If any number to divide on not clear that, the zero as a result will turn out. As we know, in the mathematician all occurs just what isn't needed: the zero turns out as a result of division of zero into any number.

We include logic of blondes and we start to think, how to us with this most "to be not clear that"? How, how? Yes in any way! We will substitute instead of a question mark a zero - and there are not problems. Then at us rather nice equations with zeroes will turn out:

a : 0 = 0

0 · 0 = a

a : 0 = 0

Here! The first and last equations coincide now and it is not necessary nothing to think out! Well, and that the zero increased by a zero at us equals to any number, means nothing. There should be whence that any numbers? It is such sleeve of the mathematician-conjurer from which it always gets them. "Let any number is given us..." All around sit, mouths поразевали, have listened openmouthed, eyes around ransack in search of any number, and mathematics in the meantime, imperceptibly, from the sleeve, gets this most any number and shows to spectators. All spectators in delight clap in palms. But we that know that in a sleeve at the mathematician division of zero into a zero is hidden. Or multiplication of a zero to a zero? Oh, with this zero absolutely it is possible to get confused.

Here we, as real mathematicians, have come to the equation:

0 : 0 = 0 · 0 = a

And after all all know that any number increased by a zero, equals to zero, instead of any number. Again at all of us will laugh. Mathematicians this problem cannot already solve some hundreds years, that already only did not think out. Now we stand near to them in a deaf corner in which ourselves have tired out ourselves and from which there is no exit, we look against each other and we wipe the snotty noses.

It is possible to put, of course, instead of a question mark an infinity badge. But what such infinity? Basically, this same any number, only very much the big. Means, this variant is not necessary.

As we see, the problem with division into a zero does not dare. Though we have come to a conclusion that the decision should be.

Let's next time try begin all with the beginning. Only not from that beginning from which, and division into a zero begins with that beginning with which the zero begins.


Division by zero is maybe!

Division by zero is considered impossible. Why? Because so mathematicians consider and learn others to think in the same way. Why mathematicians so consider? And here it is already interesting question. Everything that you will read further, can show to the friends and girlfriends, but do not take in head to show to mathematicians. Mathematicians can consider that you it is cleverer than them and terribly and cruelly to you will revenge. And you after all perfectly know that such revenge. Here when become the mathematician then can argue on a theme of division into a zero. Now we will try to understand, why division by zero is impossible?

We open a page of Wikipedia "Zero" (in Russian language) and attentively we read that to us offers collective reason. Mathematicians take number a and divide it into 0 (zero). Include the mathematical logic Further and begin reasonings. Let as a result of division the number c has turned out. In this case at number multiplication c by zero we should receive number a. But at multiplication to a zero of any number the zero as a result turns out. From this it follows that the number c cannot be result of division of number an by zero.

Personally I think hardly. We will try to write down all it easier:

a : 0 = c

c · 0 = a

Yes, really, not beautifully it turns out, especially wrong second equality. So in the mathematician does not happen. After all all know that any number increased by a zero, equals to zero.

Here it is a high time to remember a small lesson of history. Once, very long time ago, ALL considered that the Earth is a flat island in the middle of an ocean chasm which keeps on backs of three whales. This island is the World Center round which, on heavenly spheres, different features rotate: the sun, the Moon, asterisks.

Division by zero maybe! Earth on three whale. Mathematics  for blondes.
Division by zero is maybe!
Those who thought differently, it was accepted to burn on fires. Now we became more civilised, on fires we burn nobody. But to put in you the two or fill up you at examination can very simply.

And the lesson of this history says: ALL can be mistaken. If ALL around will start to be hung up, I hope, you not begin to do the same? In other words, the opinion of one person or opinion of the majority of people CAN be ERRONEOUS. If we do not acquire this lesson of history, history to us it will give once again, and once again until we will not grow wiser. Apparently, the situation with division into a zero is a repetition of lesson already passed by us.

a · 0 = 0

Now we will execute transformations and we will receive:

0 : a = 0

0 : 0 = a

The first turned out line corresponds to a mathematical rule which says that if a zero to divide into any number, the zero as a result will turn out. Concerning the second line of mathematics speak, expression a zero to divide into a zero it is not meaningful, as cannot be defined. Hi-hi, and we have defined that the zero деленный on a zero equals to any number. To which number? And what number is necessary to you, such and write. By the way, one rich dad searched to itself in the firm of chief accountant. To all applicants, besides other, it asked a question: "How many will be twice two?". For work it has accepted the person who has answered this question with the question: "And how many it is necessary to you?".

And so, mathematicians want to see concrete number, instead of the general phrase as a result of division by zero. For this reason they consider division by zero impossible. Here it is a high time to remember the second lesson of history.

You about integrals heard? If is not present, it is not terrible. It looks so: the uncertain integral something equals to something plus a constant. What is "constant"? This any number which we do not know. Yes-yes, just the same unknown number, as well as result of division by zero. So, the integral is not meaningful? Has not only sense, but also it is often applied in engineering calculations. Focus consists that the uncertain integral is only the theory. In practical calculations certain integrals are applied. When business reaches the certain integrals, all problems with a constant, that is unknown number, disappear. As a result of integration quite concrete numbers turn out.

Why it is possible to find integral and to divide into a zero it is impossible? I think that in due time engineers have come to mathematicians on a throat and the decision of a concrete problem have demanded. Mathematicians have thought up integrals and ways of their finding. It has saved to mathematicians life.

Why engineers so will not make with division by zero? To the decision of practical problems with division by zero to our engineers still as to babies to pension. Engineers simply have not grown to this level of knowledge and technics. And to mathematicians division by zero and so will descend. What difference that you to learn? Nobel Prizes do not give to them so what for once again in vain to strain.

Considering the second lesson of history, it is possible to declare with all responsibility that arguments of mathematicians concerning impossibility of division by zero are not accepted, as in a similar case with uncertain integrals were them, mathematicians, are denied.

Division by zero is maybe. We are not able to divide into a zero yet. Anything shameful in it is not present. The third lesson of history. Once people in general were not able to divide. Even number on number. Anything, have learnt both to divide, and to integrate. We will learn and on a zero to divide. Certainly, if for it us will not burn on fires. Or to arrange round us wild dances of shamans under a tambourine, inspiring us the sacred spells "Division by zero it is impossible!", "Division by zero is not meaningful!".


Zero is equal to unit

A zero is equal to unit - beautiful mathematical equality turns out. One variant of origin of similar equality did I consider in a note "Why is the factorial of zero equal to unit"? from the cycle of "Legend about mathematics". But this was just a joke on a theme a zero. Some time about this mathematical masterpiece will tell anecdotes. Statement that the factorial of zero is equal to unit it is possible bravely to attribute to the digit of mathematical funny things. But... let attentively we will look closely to equality a zero is equal to unit:

0 = 1

Looks beautifully. But there is a little problem in legitimacy of existence of similar equality - it we. Did you hear the fable of Ivan Krylov "Marmoset and glasses"?

Ivan Krylov. Marmoset and glasses. Mathematics for blondes. Nikolay Khyzhnjak.
Ivan Krylov. Marmoset and glasses.
This fable about us and about this equality. What will we do with this equality? Correctly, we will begin to stick this equality in all possible mathematical holes. Here simple example:

5 = 5 - undeniable equality, all marmosets approve amicably;

5 = 5 + 0 - was there obvious curiosity on the snouts of marmosets - now there will be something interesting, otherwise why to add a zero to the number?;

Presentiment of marmosets did not deceive - we use equality a "zero is equal to unit" and we put instead of zero unit:

5 = 5 + 1 - marmosets titter;

5 = 6 - marmosets amicably laugh at us, we in bewilderment.

"Any number is equal to any number" is the most terrible nightmare of mathematicians, which we so easily and simply got. Superstitious horror before similar equality is very well described in the story of Ted Chiang "Divizion by Zero". In this fantastic story woman-mathematician managed mathematical methods to divide a number into a zero. She got equality:

any number = any number

Finale of story "Divizion by Zero" tragic enough. But, here is a very interesting question: "Are there glasses by a that universal object which ideally goes Near ALL parts of body of marmoset?". We are not marmosets. We know a right answer - glasses are put exceptionally on a nose for the improvement of sight.

I would not begin to write about equality a "zero equal to unit", if this was the fruit of leisure fiction. But, strangely enough, it is the future of mathematics. That in what we today refuse to believe, tomorrow will be one of basic equalizations of mathematics. True, mathematics then will be other, not for monkeys with glasses.

Here little fact in support of my words. One of leading physicists-theorists, Andrei Linde, in the lecture "Many-sided Universe" said: "The sum of energy of matter and gravity energy in the scales of Universe is equal to a zero".

A zero can be equal to something, different from a zero! you will turn the special attention, that the question in this equality is about SUM, but not difference of two physical sizes. If physicists subtracted from one physical size other is be much simpler. As early as school we taught that if from something to subtract such is exact something, then as a result we will get a zero. But, physicists assure that we need to something to add something and as a result we will get a zero! The law of maintenance of energies in the scale of Universe equals a zero. Our equality a "zero is equal to unit" presents this law in a general view for any pieces, taken in the scales of universe. Strange, it turns out, what the amount of blondes in the scales of Universe must be equal to the zero... And it yet needs to be proved! Where do they, at that rate, go?!

Think, now to our marmosets not to the laughter. Does "this law of maintenance spread to all marmoset or only on her part? If on part, then on which one? If on all marmoset, then does this law operate on other marmosets? If does operate, then on all marmosets without an exception or only on select? If only on select, then who, at that rate, them does elect there? Write down and me!!! I want to be select!")))

As see, every new step in science generates mass of new questions. And for that, what not to look a marmoset with glasses, something needs to be understood. Though slightly.


What number are the natural series of numbers begun with?

The natural series of numbers are begun with a number 0 (zero). Number 0 (zero) is the least natural number.

For the Russian blondes it was farther written following. In translating into the language of blondes: the littlest natural number - it 1 (one, unit). The littlest natural number has really two names. Probably, one from a dad, second from a mother))) I will remind that in Russian mathematics zero is not a natural number!


Multiplication by zero

Multiplication by zero is possible, rules of mathematics multiplication by zero is not forbidden. Any number, multiplication by zero, will equal zero. If a whole or fractional number multiplication by zero, zero will ensue.

We will consider the example of multiplication by zero of integer. How many will it be, if 2 (two) to multiplication by 0 (zero)?

2 х 0 = 0

Decision: if 2 (two) to multiplication by 0 (zero), 0 (zero) will turn out.

Example of multiplication by zero of broken number. How many will it be, if 0,25 (zero whole twenty five hundredth) to multiplication by 0 (zero)?

0,25 х 0 = 0

Decision: if 0,25 (zero whole twenty five hundredth) to multiplication by 0 (zero), 0 (zero) will turn out.

If to multiplication a positive or negative number by zero, zero will turn out. A number zero does not have sign, therefore signs a plus or minus before zero is not put. Examples of multiplication of positive whole and fractional numbers are made a higher.

Example of multiplication by zero of negative number. How many will it be, if -2 (minus two) to multiplication by 0 (zero)?

-2 х 0 = 0

Decision: if -2 (minus two) to multiplication by zero, there will be 0 (zero).


Table division by zero

Division by zero is forbidden. Any number, positive or negative, whole or shot, to divide by zero is forbidden. Therefore a division table by zero will look so:

1 : 0 = division by zero is forbidden
2 : 0 = division by zero is forbidden
3 : 0 = division by zero is forbidden
4 : 0 = division by zero is forbidden
5 : 0 = division by zero is forbidden
6 : 0 = division by zero is forbidden
7 : 0 = division by zero is forbidden
8 : 0 = division by zero is forbidden
9 : 0 = division by zero is forbidden
10 : 0 = division by zero is forbidden

If to designate any number through а, then a division table by zero for any numbers will consist only of one line:

а : 0 = division by zero is forbidden


Division by zero

It is accepted to consider in mathematics, that division by zero not possibly, as a result of division of number by zero can not be certain. Yet mathematicians it is said that division of number by zero behaves to the mathematical operations, to not making sense. Wikipedia asserts on this occasion, that in arithmetic, division by a zero is forbidden. Therefore, when in examples there is division by zero, it is said that an example does not have a decision, as division by zero is forbidden. This mathematical rule behaves to all, even to the blondes.

It becomes firmly established in very clever mathematical books, that division by zero possibly. More precisely, mathematicians thought of sly tricks, what this division by zero to go round a side. They are sure that it succeeded them. So, if in conversation with a clever mathematician, you will hear a phrase "I am able to divide by zero!", not surprised, your interlocutor believes sincerely, that it is possible.